Use the multiplication law for logarithm to expand the following expression:[tex]log_{8} (21)[/tex]
- worth 20pt

Answers

Answer 1

Answer:

[tex]\log_8{(3)} + \log_8{(7)}[/tex]

Step-by-step explanation:

Product Rule for Logarithms

[tex]\log_b{(mn)} = \log_b{(m)} + \log_b{(n)}[/tex]

Instead of 21 you can write 3 · 7, because 21 = 3 · 7.

[tex]\log_8{(21)} = \\= \log_8{(3 \cdot 7)} =\\= \log_8{(3)} + \log_8{(7)}[/tex]


Related Questions

batman wants to wrap a perestn in a box for robin. the top and the bottom of the box is 10 cm. by 5 cm. the sides are both 3 cm by 2 cm. and the front and back are 8 cm. by 2 cm. hhow muvh wrapping papper will atman need to wrap the present?

Answers

Answer:

15

Step-by-step explanation:

What is the answer?????

Answers

Answer:

36.7075 Hz is the answer

what is the sum of first 6 terms​

Answers

Answer:

182

Step-by-step explanation:

Sum = a(r^n -1) ÷ r - 1

1(-3^6 - 1) ÷ -3 -1

= 182

r = t2 ÷ t1 * since they stated that it is geometric

12 identically sized pieces of timber are
x
cm long when put together. How long is each individual piece?

Answers

Answer:

[tex]\frac{x}{12}[/tex] (x/12)

Step-by-step explanation:

if 12 pieces combine to make x, [we know they are identical], each piece must be 1/12 of x [1/12·x = x/12]

(think of it like this: "x" length must be divided amongst 12 pieces, so, we divide x/ 12)

Answer:

Timber=x/12

Step-by-step explanation:

12 pieces long is x, if the length of each one is same, so the length of each one is x/12.

A biased dice is rolled 100 times.
The results are shown below in the table.

Result 1 2 3 4 5 6
Frequency 12 29 26 9 14 10
Estimate the probability of rolling a prime number?

Answers

Answer:

0.69 or 69% :)

Step-by-step explanation:

Prime numbers: 2, 3, 5

Now lets add :)

29 + 26 + 14

29 + 40

69

Now we add all numbers together and divide by our first number 69 :)

12 + 29 + 26 + 9 + 14 + 10

41 + 26 + 9 + 14 + 10

67 + 9 + 14 + 10

76 + 14 + 10

90 + 10

100

69/100 = 0.69 = 69% :D

Have an amazing day!!

Please rate and mark brainliest!!

find the value of x
a) 5
b) 35
c) 3
d) 7

Answers

Answer:

x=3

Step-by-step explanation:

due to its same angle of the graphic. it has to be +6 as well

23-29-35

35=11.×+2

35-2=33

33=11.×

x=3

what is the value of k such that 5x-2y=9 and 6x+ky=4 are perpendicular?

Answers

15

5x-2y=9......(1)

6x+ky=4......(2)

slope of eqn i= -5/-2

=5/2

slope of eqn ii = -6/k

since the line are perpendicular

5/2 * -6/k = -1

-30= -2k

k=15

Jane and David had identical chocolate bars.
David ate 78 of his chocolate bar.
Jane ate more of her chocolate bar than David.
What fraction of her chocolate bar could Jane have eaten?

Answers

Answer:

Step-by-step explanation:

I'm assuming you meant "David at 78% of his chocolate bar" which means he at 78/100 of his chocolate bar. So if Jane ate more she could've eaten n/100 of her chocolate bar where [tex]78 < n \leq 100[/tex]. Greater than 78 since David at 78/100 and less than or equal to 100 since 100/100 means Jane at the entire thing at 101/100 wouldn't make any sense.

There are 10 marbles in a bag. are red and the others are blue. 5 What is the ratio of red marbles to blue marbles? Question 11 * 1 There are 10 marbles in a bag . are red and the others are blue . 5 What is the ratio of red marbles to blue marbles ?​

Answers

Answer:

%50 1÷2

if there is missing information. if there is 10 total marbels 5 would be red, 5would be blue.

What is 5 ones , 38 tens , 27 hundreds , and 5 thousands? Write the number in word form and expanded form

Answers

Answer:

Eight thousand eighty five, 8000 + 80 + 5

Explanation:
Five ones, thirty-eight tens, twenty-seven hundreds, and five thousands equal to:

5 + 380 + 2700 + 5000

This is 8085 when added or eight thousand eighty-five in word form. This is also 8000 + 80 + 5 in expanded form.

Use the accompanying table to answer the questions regarding money ratios.
(a) What is the capital a 40-year-old should have with an income of $32,000?

(b) How much should a 35-year-old be saving for retirement with an income of $86,000?

(c) How much in education debt should a 30-year-old have with an income of $59,000?


The 40-year-old should have $___in capital.
(Simplify your answer)

(b) The 35-year-old should be saving $ for retirement.

(Simplify your answer)

(c) The 30-year-old should have $___ in education debt.
(Simplify your answer)
.

Answers

The 40-year-old should have $76800 in capital. The 35-year-old should be saving $$10,320 for retirement.

How to solve for the amounts

The capital that a 40 year old has to have with an income of 32000 is

capital income at age 40 * income

= 2.4 * 32000

Capital = $76800

b. At 35 the savings income has to be

percentage of savings income * income

= 12% * $86000

= $10,320

c. There is no specified value for education earnings.

Read more money ratios here:

https://brainly.com/question/16812427

What is the difference between normal definition of set and contors definition of set

Answers

Step-by-step explanation:

The collection of well defined object is called set

HEPPPPPPPPPP PLEASEEEEEEEE

Answers

Answer:

x-int=(2,0)

y-int=(0,4)

Step-by-step explanation:

m<1 = (3x + 4)º
m<2 = (3x + 4)º
m<3 = 29°
m<4 = 34°
m<5 = 25°

Answers

Answer: x = 44

Step-by-step explanation:

The exterior angles of a polygon add to 360 degrees so:

(3x+4)+(3x+4)+29+34+25=360 [forming equation]6x+96=360 [combine like terms]6x=264 [subtract 96 from both sides]x = 44 [divide both sides by 6]

find the average rate of change ​

Answers

Answer:

3rd option

Step-by-step explanation:

the average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [ 1, 4 ] , then

f(b) = f(4) = 3³ + 2 = 27 + 2 = 29

f(a) = f(1) = [tex]3^{0}[/tex] + 2 = 1 + 2 = 3 , then

average rate of change = [tex]\frac{29-3}{4-1}[/tex] = [tex]\frac{26}{3}[/tex]

Use the figure below to find the answer.
X
Find y.
y=
45
III
7
T
234567890

Answers

Answer: [tex]\frac{7\sqrt{2}}{2}[/tex]

Step-by-step explanation:

[tex]\sin 45^{\circ}=\frac{7}{y}\\\\\frac{1}{\sqrt{2}}=\frac{7}{y}\\\\y=\frac{7}{\sqrt{2}}=\boxed{\frac{7\sqrt{2}}{2}}[/tex]

Question 29 of 40
Find f(-2) for f(x) = 5.3*.

Answers

Answer:

A. [tex]\frac{5}{9}[/tex]

Step-by-step explanation:

To find f(-2) in f(x)=5*3^x, plug in -2 into all the x values.

f(-2)=5*3^-2, you can use calculator to calculate 3^-2 which equals 0.1, forever 1's.

f(-2)=5*0.1=0.5  Forever 5's.

f(-2)=0.5 or [tex]\frac{5}{9}[/tex]

Hope this helps!

If not, I am sorry.

We have two fractions, 1/6 3/8 ​ and we want to rewrite them so that they have a common denominator (and whole number numerators). What numbers could we use for the denominator? Choose 2 answers:

Answers

Answer:

See below

Step-by-step explanation:

The denominator has to be divisible by 6 and 8

  you could choose   24    48    72   96    etc

Harry used 0.75 liters of gasoline on the first day of his trip, 1.5
liters on the second, 2.25 liters on the third, and 3 liters on the
fourth. Write a function to describe the sequence, and then use
the function to predict the amount of gasoline used on the
eighth day of his trip.
Oy=0.5n; 4 L
O y = 0.75n; 6 L
Oy=n; 8L
Oy=1.5m; 12 L

Answers

The function is to describe the sequence and the amount of gasoline used on the eighth day of his trip will be y = 0.75n and 6 L respectively. Option B is correct.

What is an arithmetic sequence's sum of terms?

Each consecutive term in an arithmetic sequence has a common constant difference.

The sequence of the  liters of gasoline on each day is;

0.75,1.5,2.25,3

The given series is an arithmetic series with a common difference of 0.75

Common difference,d=0.75

First-term,a=0.75

The amount of gasoline used on the eighth day of his trip.

The nth term of the arithmetic sequence is;

[tex]\rm a_n = a+(n-1)d \\\\ \rm a_8 = 0.75+(8-1)0.75 \\\\ a_8 = 6[/tex]

The 8th term of the arithmetic sequence is 6L.

The function is to describe the sequence and the amount of gasoline used on the eighth day of his trip will be y = 0.75n and  6 L.

Hence, option B is correct.

To learn more about the arithmetic sequence refer;

https://brainly.com/question/15412619

#SPJ1

6 less than a number is less than the quotient of the number and 3.

Answers

Answer:

x<9

Step-by-step explanation:

x-6<x/3

3(x-6)<x

3x-18<x

3x-x<18

2x<18

X<18/2

X<9

evaluate the following expression when x=-4 and y=4
x³-x /4y[tex]\frac{x}{y}[/tex]

Answers

Answer: - 60

Step-by-step explanation:

[tex]\frac{(-4)^3 - (-4)}{4(4)^-4/4} \\\\= -60[/tex]

Peter uses the equation y = StartFraction 13 over 4 EndFraction x to model the number of miles that he has walked in x hours. Which statement is true about the proportional relationship that is modeled by Peter’s equation?

Answers

The statement C is true about the proportional relationship that is modeled by Peter’s equation. Peter walks at a rate of 13/4 miles per hour.

What is the equation?

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

The complete question is

"Peter uses the equation Y=13/4x to model the number of miles that he has walked in x hours. Which statement is true about the proportional relationship that is modeled by the peat there's the equation?

A: Peter walks a rate of 4/13 miles per hour.

B: Peter walks at a  rate of 4 miles per hour.

C: Peter walks at a rate of 13/4 miles per hour.

D: Peter walks at a rate of 13 miles per hour."

Given equation;

Y=13/4x

Where,

y represents the number of miles

x is the time period

The equation shows Peter walks at a rate of 13/4 miles per hour.

Hence statement C is true about the proportional relationship that is modeled by Peter’s equation.

To learn more, about equations, refer;

https://brainly.com/question/10413253

#SPJ1

Solve the inequality and express your answer in interval notation.

Answers

The correct answer is option B which is (-4-√11) and (-4+√11).

What is inequality?

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

The inequality is given as x² + 8x + 5 < 0 for we will draw a graph of the inequality and find the range of x which ranges from ( -7.31,- 0.68) So these points in the options will be equal to (-4-√11) and (-4+√11).

(-4 - √11)  = -4 -3.31 =-7.31

(-4 + √11) = -4 +3.31 = -0.68

Therefore the correct answer is option B which is (-4-√11) and (-4+√11).

To know more about inequality follow

https://brainly.com/question/24372553

#SPJ1

Directions: Find the inverse of each number.

Additive

-3 =
14 =
-28 =
-1/5 =

Multiplicative

2/3 =
6/18 =
5 =
11 =

Answers

Answer:

Step-by-step explanation:

Additive inverse:

-3=3

14=-14

-28=28

-1/5=1/5

Multiplicative Inverse:

2/3=3/2

6/18=18/6

5=1/5

11=1/11

Answer:

inverse of -3 is +3

inverse of 14 is -14

inverse of -28 is 28

inverse of -1/5 is 1/5

inverse of 2/3 is 3/2

inverse of 6/18 is 18/6

inverse of 5 is 1/5

inverse of 11 is 1/11

Step-by-step explanation:

Because inverse mean switch it. or opposite of digit

if plus digit then negative digit .

1/5 divided by 4 equals to what

Answers

Answer:

1/5 divided by 4 equals to 0.05

{x + 8y = -16
{x-3y = -5

Answers

Answer: y= -1 and x=-8

x+8y=-16

x=-8y-16

so x-3y=-5

-8-16-3y=-5

-11y-16=-5

-11y=-5+16

-11y=11

y=-1

x-3y=-5

x+3=-5

x=-8

Answer: x = -8 and y = -1

Step-by-Step Solution:

=> x + 8y = -16 (Eq. 1)
=> x - 3y = -5 (Eq. 2)

Subtracting Eq. 2 from 1, we get :-

8y + 3y = -16 + 5
11y = -11
y = -11/11
=> y = -1

Therefore, y = -1

Substitute value of ‘y’ in Eq. 2 :-

x - 3y = -5
x - 3(-1) = -5
x - -3 = -5
x + 3 = -5
x = -5 - 3
x = -5 + -3
=> x = -8

Therefore, x = -8

Hence, x = -8 and y = -1 (-8, -1)

Evaluate the expression for the given values of the variables:
2a³-7b²+ 3c - (d + e) a = 3, b = 2, c = 4, d = 11, and e = 7

Answers

Answer:

yes

Step-by-step explanation:

it's hard but you'll figure it out so don't worry

The perimeter of a rectangle is 34 cm. The length is 1 cm longer than the width. What is the length of the longest side of the rectangle?

Answers

Answer: 9 cm

Step-by-step explanation:

The formula for the perimeter of a rectangle is [tex]2l+2w=P[/tex]

Where

l is the length

w is the width

and P is the perimeter (34)

Because the length is 1 cm longer than the width instead of representing the length is l we can use w+1

Sub in the known values and solve

Step 1: Simplify both sides of the equation with the Distributive Property

[tex]2(w+1)+2w=34\\(2)(w)+(2)(1)+2w=34\\2w+2+2w=34\\(2w+2w)+(2)=34\\4w+2=34\\[/tex]

Step 2: Subtract 2 from both sides.

[tex]4w+2-2=34-2\\4w=32[/tex]

Step 3: Divide both sides by 4.

[tex]\frac{4w}{4}=\frac{32}{4} \\w=8[/tex]

Step 4: Add 1 to w to find the length of the longer side

[tex]w+1\\8+1\\9[/tex]

On a coordinate plane, a parabola opens up. It goes through (negative 8, negative 2), has a vertex at (negative 5, negative 6.5), goes through (negative 2, negative 2), and has a y-intercept at (0, 6).
Over which interval is the graph of f(x) = one-halfx2 + 5x + 6 increasing?

Answers

The graph is increasing for x > -5

Homework Progress 46 / 90 Marks Work out the length of AB. Give your answer to 3 significant figures. A (-1, 6) B (5, 3) X + Homework Progress 46 / 90 Marks Work out the length of AB . Give your answer to 3 significant figures . A ( -1 , 6 ) B ( 5 , 3 ) X +​

Answers

Answer: 6.71

Step-by-step explanation:

[tex]AB=\sqrt{(-1-5)^{2}+(6-3)^{2}} \approx \boxed{6.71}[/tex]

Other Questions
Professional practice involves applying the knowledge of kinesiology in a work setting. Group of answer choices True False a child is newly diagnosed with neonatal bronchopulmonary dysplasia (chronic lung disease). which intervention should the nurse perform first to help the parents? What is the solution to the following equation?-3+x= -8A. x = -5B. x=5C. x = 11D. x=-11 Which graph shows the solution to the system of linear inequalities? Y-3+1Helppppp 0The following table relates the weights and heights of a group of individualsparticipating in an observational study. Hint: Fill out the table first.Weight/Height Tall Medium Short Totals1828205112 25ObeseNormalUnderweightTotals14289Find the probability that a randomly chosen individual from this group is Tall. Roundyour answer to four decimal places. Difference between male and female pelvis Kaci will be an effective speaker because she has more information than anyone else. is ready to share and answer questions. has very strong opinions. possesses a loud voice. Identify the major sources of Pakistan Ideology. 6. Which of the following is a way of writing that stresses simplicity and clarify of expression?metaphorical writingPuritan Plain Styledramapoetry Producer surplus is the difference between Multiple Choice the maximum prices consumers are willing to pay for a product and the lower equilibrium price. the quantity supplied and quantity demanded at an above equilibrium price. the maximum prices consumers are willing to pay for a product and the minimum prices producers are willing to accept. the minimum prices producers are willing to accept for a product and the higher equilibrium price. Which of the following is equivalent to the radical expression below whenx>=2?(x-2)(x+9) what specific abnormality does tranexamic acid (txa) address in a trauma patient? Which line uses trochaic meter?O A. Doctor Gomez treated patients dailyOB. The greatest deed of all is helping familyOC. Fatima told me all about the dateOD. To win the bronze is still impressive Describe how Tash could negotiate with Marcus to help him see his and Kaylee's side of things. The Hudson River School was a group of artists who painted the beauty of the natural American landscape with a sense of romanticism that was embodied in the writings of _ The sum of ages of Clayman and Ato is 25 years. In five years' time, the age of Ato will twice the age of Clayman now. a. How old is Clayman? b. How old is Ato? how do you determine if a name is a variable holding a value or if it is a function call? what is the equation of a line that has a slope of -5 and a y intercept of -7 "By God," the Green Knight said, "I am gladThat I shall have from your hand what I asked for here,And that you have repeated fully, in your own words,The whole of the covenant I asked of the King:Only now you must swear to me, upon your word,That you will expect, for yourself, wherever you manageTo find me on earth, to be repaid in kindFor what you accord me today before this high company."-Sir Gawain and the Green Knight,W. S. MerwinWhich evidence shows that the Green Knight thinkshonesty is important? Check all that apply."By God, the Green Knight said"O "I am glad / That I shall have from your hand what Iasked for here""And that you have repeated fully, in your ownwords, / The whole of the covenant I asked of theKing""Only now you must swear to me, upon your word"O"wherever you manage / To find me on earth" Predict the nature of the indicatedcovalent bond.