# Logarithmic Functions Exercises

### Example 1

Solve the following exponential equation for *y*:

7^{(y + 1)} = 3*x* + 3

### Example 2

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

4*e ^{x}* + 10 = 20

### Example 3

What value of *x *satisfies the following equation?

log_{10} 10 = *x*

### Example 4

What value of *x* satisfies the following equation?

log_{3} 1 = *x*

### Example 5

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

log_{10} *x* = -3

### Example 6

Solve the following exponential equation for *y*:

*e*^{(y + 4)} – 15 = *x*^{2}

### Example 7

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

### Example 8

Evaluate the following log equation for *x* = 9:

*y* = log_{3}(*x*^{2})

### Example 9

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

*y* = ln(3*x*) + ln(*e ^{x}*)

### Example 10

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

*y* = log_{3} 13

### Example 11

Write log_{4} 17 in base-10 form.

### Example 12

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