How is the change of base formula used in solving logarithmic equations?

Answers

Answer 1

Answer:

See below

Step-by-step explanation:

The change of base formula for logarithms is [tex]\log_a(x)=\frac{\log_b(x)}{\log_b(a)}[/tex]. This formula allows us to rewrite a logarithmic expression so that the new expression contains a different base.


Related Questions

Hello people ~
what's the area of a rectangle whose width is 16m and length is 13m?​

Answers

Answer:

208 m²

Step-by-step explanation:

[tex]16 \: m\times 13 \: m = 208 \: {m}^{2} [/tex]

John goes to a restaurant and has a bill of $32.57 He uses a 10% coupon on the cost of the meal. The taxis 8%. He leaves a tip of 18% on the amount before the coupon or tax is applied. How much does he spend.​

Answers

$37.52

I know it seems close, but the coupon doesn't do much when you repay a total of 18% before the coupon.

A line has a rise of 3 and a run of 12. What is the slope?
O 1/3
O 4
O 1/4

Answers

1/4 is the answer
Explanation- 3 divided by 12 is 4 therefore 1/4 of 12 is 3 making 1/4 the slope

Find the perimeter of each figure.
6 cm
2 cm
2 cm
6 cm

Answers

Answer:

16

Step-by-step explanation:

no image, but 6 + 2 + 2 + 6 = 16

Find each real root.

Answers

Answer:

Step-by-step explanation:

I'm assuming the 7 is the question number.

The cube root is -2. There is only 1 real root.

You could find it this way. ∛(-8) = ∛-2 * - 2 * - 2

The rule for cube roots when the number has 3 roots that are the same is to take one outside the ∛ sign and discard the other 2.

-2 ∛1 The cube root of one is one.

What is the distance in inches between the 8th fret and the 5th fret

Answers

Answer:

12 inchis

Step-by-step explanation:

Scoopers ice cream shop sells one scoop of ice cream for $1.60. They sell three scoops for $4.80. How much money is needed to buy two scoops of ice cream?​

Answers

Answer:

$3.20

Step-by-step explanation:

1.60 x 2 = $3.20

You need $3.20 to buy 2 scoops of ice cream.

Answer:

Step-by-step explanation:

Since the cost of one ice cream scoop is $1.60, you would either have to add $1.60 two times, or multiply 1.60x2.


$1.60+$1.60 or 1.60x2=$3.20.

Therefore, the answer to the question would be “$3.20 would be needed to buy two scoops of ice cream.”

Use the two-way frequency table at the right to find the probability P(7th-grade boy).
(Simplify your answer.)

Answers

Answer:

8/50

Step-by-step explanation:

find the total number of 7th grade boys

put that in the numerator

I'm assuming you're trying to get the probability of picking a 7th grade boy out of all the kids in the soccer camp so 50

help i am bad at geometry

Answers

Answer:

115.5 cubic meters.

Step-by-step explanation:

First find the are which is 10.5 because are is base times width divided by 2

The multiply the are with the height. 10.5 times 11 equals 115.5 cubic meters.

Answer number 3 please

Answers

Answer:

100 cm square?

Step-by-step explanation:

1 meter square = 100 cm square

Answer:

10,000 cm²

Step-by-step explanation:

m² to cm² conversion

1 m x 1 m = 1 m²But we know : [1 m = 100 cm]100 cm x 100 cm = 10,000 cm²Therefore, 1 m² = 10,000 cm²

So, the surface area of the prism in cm² is 10,000 cm²

A scale model of a ramp is a right triangular prism as given in this figure. In the actual ramp, the triangular base has a height of 0.5 yards.

What is the surface area of the actual ramp, including the underside?

Enter your answer as a decimal in the box.



The answer is 7.2 I just didnt see anyone ask this

Answers

The surface area of the figure is 720 square inches

How to calculate the surface area of a ramp?

The surface area of a figure is the sum of all the area of its faces.

For the given diagram, it consists of 2 triangular faces and 3 rectangular faces

Surface area= (5 * 24) + 2(13*12) + 24 * 12

Surfacee area = 120  + 312 + 288

Surface area = 720 square inches

Hence the surface area of the figure is 720 square inches

Learn more on surface area here: https://brainly.com/question/76387

HELP PLEASE <3

What is the area of the circle with the equation 2x2 + 2y2 = 8?

show work pls !!

Answers

Answer:

4pi

Step-by-step explanation:

Divide through by two to get

x^2 + y^2 = 4       4 = radius squared     radius = 2

area = pi r^2 = 4 pi

Answer: 4π

Step-by-step explanation:

Under the assumption that those are exponents, and your equation is:

[tex]2x^2+2y^2=8[/tex]

You first must turn this circle equation into standard form. The standard form for the equation of a circle is as follows:

[tex](x-a)^2+(y-b)^2=r^2[/tex]

For your case, the constants 'a' and 'b' are clearly zero. We have an annoying coefficient of 2 which can be cancelled by dividing both sides by 2:

[tex]x^2+y^2=4[/tex]

If you'd like, we can write this in the following way:

[tex](x-0)^2+(y-0)^2=2^2[/tex]

So, our circle is centered at the origin (0, 0) and has a radius of 2 units. The area of a circle is given by the formula:

[tex]A=\pi r^2[/tex]

[tex]A=\pi (2^2)=4\pi[/tex]

When you are analyzing the relationship between two continuous variables, how should you plot the data?.

Answers

Answer:

Scatterplot.

Step-by-step explanation:

Scatterplots help in analyzing the relationship between two continuous variables

I need help with Function Operations

Answers

Answer:

490

Step-by-step explanation:

d(x)=700-7(30)

7x 30=210

700-210=490

therefore,

r(x)=490

5. What is the value of x and y?

a.
b.
c.
d.

Answers

Answer:

30[tex]\sqrt{2}[/tex]

Step-by-step explanation:

The triangle given is a special right triangle with angle measures as follows:

45-45-90

The side lengths for this special triangle is represented with a-a[tex]\sqrt{2}[/tex]-a[tex]\sqrt{2}[/tex]

a represents the side length that sees hypotenuse and it is 30 so x and y

30[tex]\sqrt{2}[/tex]

Find the Perimeter of each figure. Show your Solution.
(Note: No Solution considered wrong)

Answers

Answer:

1) 40 m; 2) 18 cm

Step-by-step explanation:

1) Length = 10 m

Breadth = 4 m

Perimeter of a rectangle

= length (l) × breadth (b)

= 10 × 4

= 40 m

2) Side 1 = 6 cm

Side 2 = 8 cm

Side 3 = 4 cm

Perimeter of a triangle

= Side 1 + Side 2 + Side 3

= 6 + 8 + 4

= 18 cm

_______

Hope it helps ⚜

Answer:

1. 28m

2. 18 cm

Step-by-step explanation:

Perimeter of rectangle = 2× (length + breadth )

=> 2 ( 10 + 4 )

=> 2 ( 14 )

=> 28 m

Perimeter of triangle = side a + side b + side c

=> 6cm + 8cm + 4cm

=> 18 cm

Question 8 of 10
Suppose a sample consists of the following data values. What is the sample
mean?
6,7,3,9,2,4,5,9,9,3,7,8
O A7
B. 6
C. 5

Answers

Answer:

whatever number is repeating the most is the answer.

PLEASE HELP I NEED TO GET DONE IN 10 MINUTES!!!
Marianna is painting a ramp for the school play in the shape of a right triangular prism. The ramp has dimensions as shown below. She will not paint the back or bottom surfaces of the ramp. What is the surface area of the ramp?

Answers

Answer:

3672 sq in

Step-by-step explanation:

The area painted would be 3672 sq in.

How many equilateral triangles are there in a regular hexagon.

Answers

There are total 6

Look at the attachment for proof

If we join all three diagonals we get 6 equilateral triangle

Answer:

There are 6 equilateral triangles in a regular hexagon.

Step-by-step explanation:

A regular hexagon can be dissected into 6 equilateral triangles by adding a center point .

im stuck and i need help

Answers

a right angle is always 90° and is you sum up all 3 of the angles of the triangle, you always get 180°, so:

180°-55°-90°= 35°

If 7 4/5 of the total came to 109,200, what is the total?

Answers

let’s divide this fully into 5ths to make it easier.

7 and 4/5 also equals 39/5.
39 is what we call a prime number so we can’t factor 109200 with it, so all we have left that we can do is divide.
109200/39=$2800
$2800 is 1/5 of the total, so just multiply that by 5 and you have your answer!
2800x5=$14,000.

Find the mean absolute deviation for:1, 1, 2, 4, and 7
a) 1
b) 2
c) 3
d) 0

Answers

Answer: C) 3
To get mean deviation it is nessasary to get the number between the two center numbers

If the diameter is 11, then what's the radius?

Answers

I’ll try and answer this the best as I can.

EXPLANATION: The radius of a circle is the distance from the center of the circle to any point on the circumference.

The easiest way to find the radius is by dividing the diameter in half

1/2 x 11 = 11/2 OR 5.5

ANSWER: the radius of the circle 11 cm in diameter would be 5.5 cm.


Use the points in the diagram to name the figure.

Answers

D) Line JK

<----->

JK

Hope it helps :)

I don’t understand this subject at all if you wold answer that would be a big help

Answers

Answer:

d= 8.6 ft

Step-by-step explanation:

In similar triangles, the corresponding sides are in proportion.

[tex]\boxed{\dfrac{AW}{MZ}=\dfrac{AJ}{MJ}=\dfrac{WJ}{ZJ}}[/tex]

To find the value of x,

[tex]\dfrac{AJ}{MJ}=\dfrac{WJ}{ZJ}\\\\\\\dfrac{6}{7}=\dfrac{d}{10}\\\\\\\dfrac{6}{7}*10=d[/tex]

d = 8.6 ft

Which ordered pairs match the mapping diagram? O (1, 0), (7, 2), (3, 1), (-1, 1), (-7, -6) (0, 1), (2, 7), (3, 4), 4, 1), -6, 7) O(0, 1), (0, 4), (0, 7), (2, 7), (6, 7) (0 1), (2, 7), 3, 4), (4, 1), (6, 7)​

Answers

Answer:

I've done this b4

(0, 1), (2, 7), (3, 4), (-4, 1) , (-6, 7)

What is the sum of 4 x 10-5 and 3 x 10-5 written in standard form

Answers

Answer:

7 * 10 to the power —5

Step-by-step explanation:

check out the attached photo.

Answer:

70x - 10

Step-by-step explanation:

factors and find
i) the HCF of 48,30 and 18.
ii) the LCM of 48, 30 and 18.

Answers

the gcf of 48, 30, & 18 is 6
the lcm of 48, 30, & 18 is 720

To find the probability of two
independent events, you
their
probabilities.
A) add
B) subtract
C) multiply D) divide

Answers

Answer:

To find a probability Multiply two independent events.

Find the y-intercept and the slope of the line.
Y=-4x-3

Answers

Answer:-

Slope:-

-4

y-intercept:-

(0,-3)

Solution:-The equation of this line is written in Slope-Intercept Form, which looks like so:-y=mx+bIn this formula, m stands for the slope of the line, and b stands for the y-intercept.Please remember that the slope is the line's rise (the amount of units we move up, or "rise" divided by its run (the amount of units we move left or right, and the y-intercept is the point where the line intersects the y-axis. (0, b)Also, please notice that m is the coefficient of x, and b is the constant.Therefore, the slope of the line is equivalent to -4, and the y-intercept is (0, -3).

Hope it helps.

Do comment if you have any query.

Answer:

Slope: 4; y-intercept: -3

Explanation:

To find the slope of the line, we will look at the number in front of x.

That number is -4. Hence, the slope is -4

Now, the y-intercept is the constant.

The constant is -3.

Hence, the y-intercept is -3.

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