# Logarithms and Exponential Functions

Logarithmic Functions Exercises

# Logarithmic Functions Exercises

### Example 1

Solve the following exponential equation for y:

7(y + 1) = 3x + 3

### Example 2

Find x in the following exponential equation. Do not simplify to decimals:

4ex + 10 = 20

### Example 3

What value of x satisfies the following equation?

log10 10 = x

### Example 4

What value of x satisfies the following equation?

log3 1 = x

### Example 5

Is the following logarithmic equation valid for any one value of x?

log10 x = -3

### Example 6

Solve the following exponential equation for y:

e(y + 4) – 15 = x2

### Example 7

Solve the logarithmic equation  for x. Do not simplify to decimals.

### Example 8

Evaluate the following log equation for x = 9:

y = log3(x2)

### Example 9

Evaluate the following log equation for x = 5, to three decimal places:

y = ln(3x) + ln(ex)

### Example 10

Evaluate the following log equation to three decimal places using only base-10 logarithmic functions:

y = log3 13

### Example 11

Write log4 17 in base-10 form.

### Example 12

Write ln(4x) in base-10 form.