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# Logarithms and Exponential Functions

Properties of Exponents and Logarithms Exercises

# 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 expression correct?

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

### Example 3

Is log4 16 equivalent to 2 log4 8?

### Example 4

Combine the following log functions into one function:

log 7 – log(8x) – log(4x + 6)

### Example 5

Combine the following log functions into one function:

log x2 + log y – log y2

### Example 6

Solve e6xe -7x = y for x.

### Example 7

Expand the following log function:

log5(4xy)

### 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 = log7(100x2)

### Example 10

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

y = ex4x

### Example 11

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

log(x2 + 4x + 4)

### Example 12

Simplify the following log function and solve for z:

4 = log x2 + log y + log z

### Example 13

Expand the following log function:

ln[(4x2y)/(z1/2)]