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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 function correct: log (9x + 4) = log 9x + log 4

### Example 3

Is y = log4 16 equivalent to y = 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

Simplify the following equation: xe4xe-7x = y

### Example 7

Expand the following log equation, and write it using only base-10 logarithmic functions: y = log7 (5x – 4)(2x + 3)

### Example 8

Expand the following log function: log5 4xy

### 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 = log7 100x2

### Example 11

Convert the following exponential equation to natural logarithmic form, then simplify irrationals to three decimal places: y = ex4x

### Example 12

Simplify the following log function: log (x2 + 4x + 4)

### Example 13

Simplify the following log function and solve for z: 4 = log x2 + log y + log z

### Example 14

Expand the following log function: ln (4x2y/z1/2)