A company bought a photocopier for R150 00 on 1 july 2022,they will use the old photocopier as a trader in when they replace it with the a similar new photocopier in 5 years time on 2027.
calculate the trade in value of the old photocopier after 5 years,if it depreciates at a rate of 9% p.a on straight line method.
Answers
Answer:
do it yourself what do you do while teacher is teaching
Related Questions
Makayla’s local movie theater has a moviegoer club. The charts in the annual registration fee of $25. However movie tickets are discounted remembers at six dollars per ticket instead of the regular nine dollars per ticket. Let him represent the number of movie tickets Makayla’s purchase a need to write a function tomorrow the amount of money Makayla spent going to the movies doing the club
Answers
Answer:
m = 25 + 6n
Step-by-step explanation:
To write a function for the amount of money Makayla spent going to the movies during the club, you need to consider two things: the annual registration fee and the discounted ticket price. The annual registration fee is a fixed amount that does not depend on the number of movie tickets Makayla purchases. The discounted ticket price is a variable amount that depends on the number of movie tickets Makayla purchases. You can use a letter, such as n, to represent the number of movie tickets Makayla purchases. Then, you can write an expression for the amount of money Makayla spent on movie tickets, which is 6 times n, or 6n. To find the total amount of money Makayla spent going to the movies during the club, you need to add the annual registration fee and the amount of money spent on movie tickets. This gives you the expression 25 + 6n. You can use another letter, such as m, to represent the total amount of money Makayla spent going to the movies during the club. Then, you can write an equation that relates m and n, which is m = 25 + 6n. This equation is a function that models the amount of money Makayla spent going to the movies during the club as a function of the number of movie tickets she purchased.
{1, √2, √√3, 2, √5, ...}
need help knowing the sequence and the 3 next terms
Answers
Answer:
3, 2√2, √7
Step-by-step explanation:
compute the square roots of the next three prime numbers:
√7
√11
√13
Therefore, the next three terms of the sequence are:
{1, √2, √3, 2, √5, √7, √11, √13}
chatgpt
chat
Si la secuencia es 7,12,17,22 y la regla es agregar 5 cuales son los siguentes dos terminos ?
Answers
the next two terms in the sequence would be 12 and 17.
The figure on the right shows the cross-section of a pipe. The internal radius is 5cm and the thickness of the metal is 6mm. What is the external circumference of the pipe? (Take π = 22)
Answers
The external circumference of the metal pipe is approximately 31.4 centimeters.
We know that the circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
The circumference of the circle = 2πr
We are given that internal radius is 5cm and the thickness of the metal is 6mm.
The circumference of the external circle = 2πr
= 2 x 3.14 x 5
= 31.4
The circumference of the metal pipe is approximately 31.4 centimeters.
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A certain disease has an incidence rate of 0.4%. If the false negative rate is 6% and the false positive rate is 4%, compute the probability that a person who tests positive actually has the disease.
Give your answer accurate to at least 3 decimal places
Answers
D= the event that a person has the disease
D'= the event that a person does not have the disease
T+ - the event that a person tests positive
T-= the event that a person tests negative
We are given that the incidence rate of the disease is 0.4%, which means P(D) = 0.004. We
are also given the false negative rate, which means P(T-ID) = 0.06, and the false positive rate,
which means P(T+|D') = 0.04
We want to compute the probability that a person who tests positive actually has the disease, which is given by Bayes' theorem:
P(DIT+) = P(T+|D)P(D) / [P(T+|D)P(D) + P(T+[D')P(D)]
To compute this probability, we need to compute P(T+|D) and P(T+|D'):
P(T+ID) = 1 - P(T-|D) = 1 - 0.06 = 0.94
P(T+|D') = false positive rate = 0.04
Now we can substitute these values into Bayes' theorem:
P(DIT+) = (0.94)(0.004) / [(0.94)(0.004) + (0.04)(1 - 0.004)]
=0.0853
Therefore, the probability that a person who tests positive actually has the disease is 0.0853 or approximately 0.085 to 3 decimal places
Urgent!!!!!
Help guys I need to answer the questions a. b. c. d. e.
I would appreciate it.
Answers
a. The concentration would be 0.5 mg/L at approximately t = 40 hours.
b. The table representing the concentration of the drug in the bloodstream, t hours after administration is shown below.
c. A reasonable domain for this function is t ≥ 0.
d. The patient should receive the next intravenous dose of the drug in order to maintain a concentration above 1 mg/L and below 8 mg/L at t = 1.25 hour.
e. The concentration of the oral drug and the concentration of the intravenous drug would keep increasing over the first 20 hours after it is administered.
How to calculate when the concentration will be 0.5 mg/L?In order to determine the time when the concentration would be 0.5 mg/L, we would substitute the value of the concentration and then solve the quadratic function for time (t);
c(t) = 20t/(t² + 4)
0.5 = 20t/(t² + 4)
0.5(t² + 4) = 20t
0.5t² + 2 = 20t
0.5t² + 2 - 20t = 0
t² + 4 - 40t = 0
t² - 40t + 4 = 0
Time, t = 38.8998 ≈ 40 hours.
Part b
In this context, we would complete the table of values at various time (t) as follows;
t 0 2 4 6 8 10 12 14 16 18 20
c(t) 0 5 4 3 2.35 1.92 1.62 1.4 1.23 1.10 1.00
Part c
Since the concentration of the drug at time, t = 0 is equal to 0 mg/L and the concentration actually never becomes zero (0) for any value of time (t), we can reasonably infer and logically deduce that a reasonable domain for this quadratic function is t ≥ 0 or {0, ∞}.
Part d and e
Furthermore, the intravenous drug must be administered to the patient between the time interval 1.25 ≤ t ≤ 20 in order to maintain a concentration above 1 mg/L and below 8 mg/L.
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Find the value of the missing coefficient in the factored form of 27f^3+125g^3=(3f+5g)(9f^2-?fg+25g^20
Answers
The value of the missing coefficient is 12
Lets explain how to factorize the difference of two cubes
- The factorization of the difference of two cubes like a³ - b³, is a
product of a binomial and trinomial
- The binomial is the cube root of the first term and the second term
∵ The ∛a³ = a and ∛b³ = b
∴ The binomial is (a - b)
- We will find the trinomial from the binomial by square the 1st term
of the binomial and multiply the 1st term and the 2nd term of the
binomial with opposite sign of the binomial and square the 2nd
term of the binomial
∴ The trinomial is (a² + ab + b²
∴ The factorization of (a³ - b³) is (a - b)(a² + ab + b²)
* Lets solve the problem
∵ 8f³ - 216g³ is the difference of two cubes
∵ ∛(8f³) = 2f
∵ ∛(216g³) = 6g
∴ The binomial is (2f - 6g)
- Lets make the trinomial
∵ (2f)² = 4f²
∵ (2f)(6g) = 12fg
∵ (6g)² = 36g²
∴ The trinomial = (4f² + 12fg + 36g²)
∴ The factorization of 8f³ - 216g³ = (2f - 6g)(4f² + 12fg + 36g²)
∴ The value of the missing coefficient is 12.
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complete question:
Find the value of the missing coefficient in the factored form of 8f^3-216g^3
8f^3-216g^3=(2f-6g) (4f^2+?fg+36g^2)
The value of ? =
Three brothers share some money. The oldest 5/11 of the money. The next boy gets gets 7/12 of the remainder. What fraction of the money does the youngest boy get?
Answers
The fraction of the money the youngest boy does get is 5x/22.
Given that, three brothers share some money. The oldest 5/11 of the money.
Let the total money be x.
Share of oldest boy = 5/11 ×x
= 5x/11
Remainder = x-5x/11
Remainder = 6x/11
The next boy gets 7/12 of the remainder.
Share of next boy = 7/12 × 6x/11
= 7x/22
Share of youngest boy = 6x/11 - 7x/22
= (12x-7x)/22
= 5x/22
Therefore, the fraction of the money the youngest boy does get is 5x/22.
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Triangle A’B’C is a dilation of triangle ABC. Find the scale of the dilation.
Answers
The scale of the dilation is 7/15.
The scale of dilation between two similar figures is the ratio of their corresponding side lengths. In this case, since triangle A'B'C is a dilation of triangle ABC, we can find the scale of dilation by comparing the corresponding side lengths.
Let's say that the scale of dilation is k. Then we can write:
AB' = k × AB
AC' = k × AC
BC' = k × BC
To find k, we can choose any two corresponding sides and set their ratio equal to k. For example, we can choose AB' and AB, and write:
AB' / AB = k
So, AC' / AC = 7/15
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What units do we use when calculating surface area
A-Units
B-SquareUnits
C-CubicUnits
Please help
Answers
Answer:
B
Step-by-step explanation:
square units (units for all area)
how to answer the question?
Answers
Answer:
A
Step-by-step explanation:
Note that the digit 5 in 50321 represents 50000 whereas the digit 5 in 42570 represents 500.
So, the total value is:
[tex]50000+500=50500[/tex]
Answer:
Step-by-step explanation:
1. 60mi/h a km/min
2. 75km/h a m/s
3. 80km/h a mi/h
4. 100km/h a m/s
Answers
The solution to the conversions are: (1) 1.60934 km/min, (2) 20.8333 m/s, (3) 49.7097 mi/h, (4) 27.7778 m/s, (5) 118100.64 ft/h
Conversion of Units1. 60mi/h to km/min
First, convert miles to kilometers:
1 mile (mi) = 1.60934 kilometers (km)
60mi/h = 60 x 1.60934 = 96.5604km/h
Next, convert hours to minutes:
1 hour = 60 minutes
96.5604 km/h = 96.5604 km/h x (1 h / 60 min)
= 1.60934 km/min.
Therefore, 60 mi/h is equal to approximately 1.60934 km/min.
2. 75km/h to m/s
First, convert kilometers to meters:
1 kilometer = 1000 meters
75 km/h = 75 km/h x (1000 m / 1 km)
= 75000 m/h
Next, convert hours to seconds:
1 hour = 3600 seconds
75000 m/h = 75000m/h x (1 h / 3600 s)
= 20.8333 m/s.
Therefore, 75 km/h is equal to approximately 20.8333 m/s.
3. 80km/h to mi/h
First, convert kilometers to miles:
1 mile = 1.60934 kilometers
1 kilometers = (1/1.60934) mile
80 km/h = 80km/h x (1 mi / 1.60934 km)
= 49.7097 mi/h.
Therefore, 80 km/h is equal to approximately 49.7097 mi/h.
4. 100km/h to m/s
First, convert kilometers to meters:
1 kilometer = 1000 meters
100 km/h = 100km/h x (1000 m / 1 km)
= 100000 m/h.
Next, convert hours to seconds:
100000 m/h = 100000 x (1 h / 3600 s)
= 27.7778 m/s.
Therefore, 100 km/h is equal to approximately 27.7778 m/s.
5. 10m/s to ft/h
First, convert meters to feet:
10 m/s = 10 x (3.28084 ft / 1 m)
= 32.8084 ft/s.
Next, convert seconds to hours:
32.8084 ft/s = 32.8084 x (3600 s / 1 h)
= 118100.64 ft/h.
Therefore, 10 m/s is equal to approximately 118100.64 ft/h.
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Why is the interest rate of a loan one of the most important things to consider when shopping around for loans?
a.
The interest rate should be ignored, because there’s nothing a consumer can do to change it.
b.
The interest rate is essentially how long you have to pay off your loan, and the shorter the better.
c.
The interest rate can drastically change the total amount paid to the lender, in the case of mortgages, up to thousands of dollars.
d.
The interest rate does not change, even between banks, so choosing the right time to borrow is essential.
Answers
The interest rate can drastically change the total amount paid to the lender, in the case of mortgages, up to thousands of dollars.The correct answer is c.
The interest rate of a loan is one of the most important factors to consider when shopping around for loans because it directly affects the cost of borrowing money. The interest rate determines the percentage of the loan amount that the borrower will have to pay back to the lender as interest over the loan's term.
A higher interest rate means that borrowers will have to pay more in interest over the life of the loan, increasing the total cost of borrowing. Conversely, a lower interest rate will result in lower interest payments and a reduced overall cost of the loan.
For example, in the case of a mortgage, which is a long-term loan, even a small difference in the interest rate can have a significant impact on the total amount paid to the lender. Over the course of a 30-year mortgage, a higher interest rate could result in thousands of dollars in additional interest payments.
Therefore, it is important to compare and consider different loan offers to find the best interest rate available. This can help borrowers save money and make more informed decisions about their borrowing options. The correct answer is c.
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After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the
rainbow is the shape of a parabola.
The equation for this parabola is y=-x² + 36
1.Create a table of atleast 4 values of the function that includes two points of intersection between the airplane and the rainbow
2.What is the domain and range of the rainbow? Explain what the domain and range represent.Do all of the values make sense in the situation. Why or why not.
3.what are the x and y intercepts of the rainbow. Explain what each intercept represents.
Answers
Answer:the values is y x 2= the domain is no it does not make sense because it as nothing to do with the shape of the rainbow
Step-by-step explanation:
The half-life of strontium-90 is
approximately 29 years. How much of a
150 g sample of strontium-90 will remain
after 116 years?
Remaining Amount = 150(1 - [?])
Remaining Amount = [(1 - r)t
0.
Enter
Answers
The amount of the 150 g sample of the strontium-90 that will remain after 116 years, with the half-life of strontium-90 of 29 years, is about 9.375 grams
What is the half-life of a substance?The half-life of a (radioactive) substance is the duration it takes or required for half of the substance to decay into
The formula for exponential decay indicates that we get;
Amount remaining = Initial amount × (1/2)^(t/h)
Where;
t = The duration that elapses = 116 years
h = The half-life of the substance = 29 years
The initial amount of the strontium-90 = 150 g
Therefore; Amount remaining = 150 × (1/2)^(116/29) = 9.375
The amount of the strontium-90 that will remain after 116 years is 9.375 grams
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Six more than twice what number is 36
Answers
Answer:
15
Step-by-step explanation:
36-6=30
30/2= 15
15x+6=36
find the perimeter of ABC
Answers
The perimeter of the triangle ABC is 146.
Given that a triangle we need to find it perimeter,
We know that the tangents from a common point to the circle are equal,
Therefore,
DB = BE
EC = FC
FA = AD
So,
FA = AC - FC
FA = 52-13 = 39
Therefore,
FA = AD
AD = 39
Now,
9x-56 = 17x - 120
8x = 64
x = 8
DB = BE = 16
AB = 16 + 39 = 55
BC = 16+13 = 29
AC = 52
Perimeter = AC + BC + AB = 55 + 29 + 52 = 146
Hence the perimeter of the triangle ABC is 146.
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What is the exact value of cos 30°?
Enter your answer, as a simplified fraction, in the box.
Answers
cos 30° can be evaluated using the trigonometric identity: cos 30° = cos(π/6) = (√3)/2.
Therefore, the exact value of cos 30° is (√3)/2.
Answer:
cos30 = √3 / 2
or cos30 ≈ 0.8660254037
what number is 4 in the number 4,120,375
Answers
Answer:
It is 4 million or Million
because the place it is in is called million.
pls help guys calculus 30pts
Answers
3x *5 ≤23 give the value of x
Answers
X=1.5
Convert the following binary to decimal numbers 1112
Answers
[tex]1\cdot2^2+1\cdot2^1+1\cdot2^0=4+2+1=7\\\\111_2=7_{10}[/tex]
Urgent!!!!!
Help guys I need to answer the questions
I would appreciate it.
Answers
The function for the concentration of the drug in the bloodstream indicates;
a. The concentration will be 0.5 mg/L when t = 20 - 6·√(11) and t = 20 - 6·√(11) hours
b. Please find the completed table of values in the following section
c. The domain is all positive values of t, including t = 0, which is [0, ∞)
d. The patient should receive the drug after about 19.78 hours
e. The shape of the concentration graph are similar, but the concentration of the oral drug is higher than the concentration of the drug administered intravenously
What is a function?A function is a rule that maps input variables to output values.
a. The function modelling the concentration of the drug in the bloodstream after t hours indicates;
c(t) = 20·t/(t² + 4)
When the concentration is 0.5 mg/L, we get;
c(t) = 20·t/(t² + 4) = 0.5
(t² + 4) × 0.5 = 20·t
t² + 4 = 20·t ÷ 0.5 = 40·t
t² - 40·t + 4 = 0
t = (40 ± √((-40)² - 4 × 1 × 4))/(2 × 1) = (40 ± 12·√(11))/(2) = 20 ± 6·√(11)
The concentration will be 0.5 mg/L when t = 20 + 6·√(11) and t = 20 - 6·√(11)
b. The completed table of values, obtained using MS Excel can be presented as follows;
t [tex]{}[/tex] 0 2 4 6 8 10 12 14 16 18 20
c(t) [tex]{}[/tex]0 5 4 3 2.35 1.92 1.62 1.4 1.23 1.09 0.99
c. The denominator, t² + 4, indicates that the denominator is positive for all values of x, whereby the time is a natural, a possible domain for the function is the set [0, ∞)
d. The values in the table indicates that to maintain a concentration above 1 mg/L and below 8 mg/L, the patient must receive the next intravenous dose between the values obtained as follows;
The maximum value of the function is 5 mg/L when t = 2 hours, therefore, when c(t) = 1 mg/L, we get;
c(t) = 20·t/(t² + 4) = 1, which indicates that t = 10 ± 4·√6, which indicates that the time at which the concentration reduces to 1 mg/L again in the bloodstream is 10 + 4·√6 ≈ 19.78 hours
The patient should receive the next dose, after about 19.78 hours
e. The concentration of the oral drug, obtained from a similar question on the website, indicates that the maximum concentration is 64 mg/L, which is higher than the maximum concentration of the drug administered intravenously, which has a maximum concentration of 5 mg/L
However, the maximum bloodstream is reached at about the same period for both drugs administration methods
The concentration of the drug administered by oral administration in the first part is about four times the drug administered intravenously after 20 hours.
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HELPP
If you pour a cup of coffee that is 200F, and set it on a desk in a room that is 68F, and 10 minutes later it is 145F, what will the temperature be 15 minutes after you originally poured it?
Answers
To solve this problem, we can use Newton's law of cooling, which states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. We can use the formula:
T(t) = T_s + (T_0 - T_s) * e^(-kt)
where:
T(t) is the temperature of the coffee at time t
T_s is the temperature of the surroundings (68F)
T_0 is the initial temperature of the coffee (200F)
k is a constant that depends on the specific heat transfer properties of the coffee and its container
e is the mathematical constant e, approximately 2.71828
We can use the fact that the temperature is 145F after 10 minutes to find the value of k:
145 = 68 + (200 - 68) * e^(-10k)
e^(-10k) = (145 - 68) / (200 - 68) = 77 / 132
-10k = ln(77/132)
k = -ln(77/132) / 10
Now we can use this value of k to find the temperature of the coffee after 15 minutes:
T(15) = 68 + (200 - 68) * e^(-k*15)
T(15) = 68 + (200 - 68) * e^(-15ln(77/132)/10)
T(15) = 111.72
Therefore, the temperature of the coffee 15 minutes after it was poured would be approximately 111.72F.
Answer:
127 F
Step-by-step explanation:
we will use newton's law of cooling to understand the process. Since the coffee here is losing heat so the heat loss will be proportional to the temperature difference
The gravitational pull of the Moon is not as great as that on Earth. In fact, if a person checks their weight on the Moon, it will be only of their weight on Earth. 6. What does each ordered pair on the line represent? 7. Write an equation to represent the relationship shown in the graph. Weis 8. Is this a proportional relationship? Justify your answer. 9. In this problem situation, do all the points on the graph make sense? 10. Determine the weight of a person on Earth given his weight on the Moon. a. 12 lb b. 21 lb c. 36 lb 330 310 Weight on Moon (pounds) 0 30 60 90 120 150 180 210 240 270 Weight of Astronaut Without Shuttle Suit (pounds) 222262 32 28 24 20 16 12 8 4 Weight on Earth Versus Weight on Moon 0 20 40 60 80 100 120 140 160 180 Weight on Earth (pounds) LESSON 2: The Power of the Horizontal Line
Answers
6. Each ordered pair on the line represent the weight on Earth (pounds) and weight on Moon (pounds).
7. An equation to represent the relationship shown in the graph is [tex]y=\frac{1}{6} x[/tex].
8. Yes, this a proportional relationship.
9. In this problem situation, it is not all the points on the graph that make sense.
10. a. The weight of a person on Earth given a weight of 12 lb on the Moon is 72 lb.
b. The weight of a person on Earth given a weight of 21 lb on the Moon is 126 lb.
c. The weight of a person on Earth given a weight of 36 lb on the Moon is 216 lb.
What is a proportional relationship?In Mathematics, a proportional relationship produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
k is the constant of proportionality.y represent the Weight on Moon (pounds).x represent the Weight on Earth (pounds).Part 7.
Next, we would determine the constant of proportionality (k) based on the data points provided as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 10/60 = 20/120 = 30/180 = 40/240
Constant of proportionality, k = 1/6.
Therefore, the required equation is given by;
y = kx
y = x/6
Part 8.
Since the data points have a constant of proportionality, yes, it is a proportional relationship.
Part 9.
By critically observing the graph, it is not all the data points on the graph that make sense
Part 10.
a. When y = 12 lb, the weight of a person on Earth is given by;
x = 6y
x = 6(12)
x = 72 lb.
b. When y = 21 lb, the weight of a person on Earth is given by;
x = 6y
x = 6(21)
x = 126 lb.
c. When y = 36 lb, the weight of a person on Earth is given by;
x = 6y
x = 6(36)
x = 216 lb.
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Find the value of x.
Answers
Answer: x = 11
Step-by-step explanation:
We know that vertical angles are congruent to each other. We will create an equation to help us solve. Then, will isolate the x-variable with inverse operations.
128° = 8x + 40°
8x + 40° = 128°
8x = 88°
x = 11
select ALL the correct answers.
Which data set could be used to create the box plot below?
Answers
Im sorry but I dont see a Box Plot.
Answer:
provide more data
Step-by-step explanation:
no solution
Based on the values in the table below, find the slope and y-intercept to write the equation of the line in the form y=mx+b.
Answers
The y-intercept of the line is 2. the equation of the line in the form y=mx+b is y = 2x + 2.
To find the equation of the line in the form y=mx+b, we need to first find the slope (m) and the y-intercept (b).
Looking at the table:
x | y
--|--
1 | 4
2 | 6
3 | 8
We can use the formula for slope:
m = (y2 - y1) / (x2 - x1)
Let's use the first two points (1, 4) and (2, 6):
m = (6 - 4) / (2 - 1)
m = 2 / 1
m = 2
So the slope of the line is 2.
To find the y-intercept, we can use the formula:
b = y - mx
Let's use the first point (1, 4) and the slope we just found:
b = 4 - (2)(1)
b = 4 - 2
b = 2
So the y-intercept of the line is 2.
Putting it all together, the equation of the line in the form y=mx+b is:
y = 2x + 2.
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What is the average of the points A, B and C with weights 1, 4 and 1
respectively?
Answers
The weighted average of the points A, B, and C with weights 1, 4, and 1 respectively is (A + 4B + C) / 6.
To find the weighted average of the points A, B, and C with weights 1, 4, and 1 respectively, we first need to multiply each point by its corresponding weight and then add them together.
Finally, we divide the sum by the total weight.
The weighted sum of the points is:
(1 × A) + (4 × B) + (1 × C) = A + 4B + C
The total weight is:
1 + 4 + 1 = 6
Therefore, the weighted average of the points A, B, and C with weights 1, 4, and 1 respectively is:
(A + 4B + C) / 6
Note that the weight of B is four times that of A and C.
Therefore, the weighted average will be closer to B than A or C, reflecting the fact that B has a larger weight.
For example, if A = 3, B = 5, and C = 4, then the weighted average is:
(A + 4B + C) / 6 = (3 + 4 × 5 + 4) / 6 = 26 / 6 = 4.33.
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If log10^2=m and log10^3=n, find log10^24 in term of m and n
Answers
let's recall that whenever omitted, the base is assumed to be 10.
[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\log_{10}(2)=m\implies \log(2)=m\hspace{5em}\log_{10}(3)=n\implies \log(3)=n \\\\[-0.35em] ~\dotfill\\\\ \log_{10}(24)\implies \log(24)\implies \log(8\cdot 3)\implies \log(2^3\cdot 3) \\\\\\ \log(2^3)+\log(3)\implies 3\log(2)+\log(3)\implies 3m+n[/tex]
