# Logarithms and Exponential Functions

# Linking Exponents and Logarithms Exercises

### Example 1

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

### Example 2

What is the inverse function of *y* = ln *x*?

### Example 3

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

### Example 4

What is the inverse function of (5*xy* + *x*)^{2} = *x*^{4}

### Example 5

Is *x*^{-1} equivalent to

### Example 6

Is *y* = 4^{x} the inverse of log_{x} 4 = *y*

### Example 7

If the inverse of a function *y* = *f*(*x*) is *y*= *g*(*x*), what does *f*(*g*(*x*)) and *g*(*f*(*x*)) both equal?

### Example 8

What is the inverse function of log_{4} (3*x* + 2)?

### Example 9

What is the inverse function from the set {1,4; 3,10 ; 6,19}?

### Example 10

Is the following function one-to-one: x^{2}?

### Example 11

What is the log form of the exponential function y = 4^{x} – 3?

### Example 12

What is the log form of the exponential function *y *= 10*e*^{x}?

### Example 13

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

### Example 14

Is the following function one-to-one: *x*^{3} + 4?

### Example 15

Which domains can this function be one-to-one in? 2*x*^{2} – 4