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# Logarithms and Exponential Functions

# 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 *fulfills the following equation: log_{10} 10 = *x*

### Example 4

What value of *x *fulfills 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

Simplify the following exponential equation for *y*: *e*^{y + 4} – 15 = x^{2}

### Example 7

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

### Example 8

Evaluate the following log equation for *x* = 3, to three decimal places: *y* = log_{3} (*x*^{2}) + log_{3}(2*x* + 3) + log_{3}8*x*

### 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* = log_{3} 13

### Example 11

Write the following logarithmic equation in base 10 form: log_{4}17

### Example 12

Write the following logarithmic equation in base 10 form: ln 4*x*