# Properties of Exponents and Logarithms Exercises

### Example 1

Combine the following log functions into one function:

log 4 + log(*x* – 3) + log(2*x* + 4)

### Example 2

Is the following expansion of a logarithmic expression correct?

log(9*x* + 4) = log(9*x*) + log 4

### Example 3

Is log_{4} 16 equivalent to 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

Solve *e*^{6x}*e*^{ -7x} = *y* for *x*.

### Example 7

Expand the following log function:

log_{5}(4*xy*)

### Example 8

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

### Example 9

Simplify the following log function to a form without exponents, then change to base-10:

*y* = log_{7}(100*x*^{2})

### Example 10

Convert the following exponential equation to natural logarithmic form, then simplify irrationals to three decimal places:

*y* = *e ^{x}*4

^{x}### Example 11

Simplify the following log function so there aren't any squared terms:

log(*x*^{2} + 4*x* + 4)

### Example 12

Simplify the following log function and solve for *z*:

4 = log *x*^{2} + log *y* + log *z*

### Example 13

Expand the following log function:

ln[(4*x*^{2}*y*)/(*z*^{1/2})]