Linking Exponents and Logarithms Exercises

Example 1

What is the inverse function of y = log 4x ?

Hint

Try exponentiation.

Example 2

What is the inverse function of y = ln x?

Hint

Which irrational number does ln have in its base?

Example 3

What is the inverse function of y = 15x + 3?

Hint

Solve for the dependent variable first.

Example 4

What is the inverse function of y = 5x + 1?

Hint

Just solve for x, then swap those variables.

Example 5

Is y = 4^x the inverse of log_x 4 = y?

Hint

What does the base of the logarithm represent?

Example 6

If f(x) = 2x + 2, what is f(f^-1(x))?

Hint

Find the inverse, then plug the entire inverse into the original function.

Example 7

What is the inverse function of y = log₄ (3x + 2)?

Hint

Start by rewriting the equation as 4^y = 3x + 2.

Example 8

What is the inverse function of y = 3x + 1?

Hint

Don't forget to make those variables swap places.

Example 9

Is f(x) = x² a one-to-one function?

Hint

Will squaring -2 and 2 (or the positive/negative values of any number) give the same answer?

Example 10

Solve for x:

y = 4^x – 3

Hint

It's like finding the inverse, but not quite.

Example 11

Solve for x:

y = 10e^x

Hint

It's au naturel, right? Try dividing both sides by 10, then taking the natural log of both sides.

Example 12

What is the inverse function of y = 7^{(x + 10)}?

Hint

Don't worry, exponentiation won't hurt the exponent on the 7.

Example 13

Is the following function one-to-one?

f(x) = x³ + 4

Hint

Graph me and see!

Example 14

How should we restrict the domain of this function to make it one-to-one?

f(x) = 2x² – 4

Hint

When will the horizontal line test pass?

Linking Exponents and Logarithms Exercises

Linking Exponents and Logarithms Exercises

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Example 9

Example 10

Example 11

Example 12

Example 13

Example 14

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