# Logarithms and Exponential Functions

# Properties of Exponents and Logarithms Exercises

### Example 1

Combine the following log functions into one function: log 4 + log (x – 3) + log (2x + 4)

### Example 2

Is the following expansion of a logarithmic function correct: log (9*x* + 4) = log 9*x* + log 4

### Example 3

Is *y* = log_{4} 16 equivalent to *y* = 2 log_{4} 8?

### Example 4

Combine the following log functions into one function: log 7 – log 8*x* – log (4*x* + 6)

### Example 5

Combine the following log functions into one function: log (*x*^{2}) + log *y* – log *y*^{2}

### Example 6

Simplify the following equation: *xe*^{4x}*e*^{-7x} = *y*

### Example 7

Expand the following log equation, and write it using *only* base-10 logarithmic functions: *y* = log_{7} (5*x* – 4)(2*x* + 3)

### Example 8

Expand the following log function: log_{5} 4*xy*

### Example 9

Expand the following log function, then simplify irrationals to three decimal places:

### Example 10

Simplify the following log function to a form without exponents, then change to base 10: *y* = log_{7} 100*x*^{2}

### Example 11

Convert the following exponential equation to natural logarithmic form, then simplify irrationals to three decimal places: *y* = *e*^{x}4^{x}

### Example 12

Simplify the following log function: log (*x*^{2} + 4*x* + 4)

### Example 13

Simplify the following log function and solve for *z*: 4 = log *x*^{2} + log *y* + log *z*

### Example 14

Expand the following log function: ln (4x^{2}y/z^{1/2})