Logarithmic Function Manipulation Worksheet

Logarithmic Function Manipulation

Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. Evaluate the following logarithms:

a) log₂ 16

b) log₃ (1/9)

c) log₁₀ 1000

d) ln(e⁵)

2. Complete the following statements using the properties of logarithms:

a) logb (MN) =  

b) logb (M/N) =  

c) logb (Mᵖ) =  

d) logb b =  

e) logb 1 =  

3. Expand the following logarithmic expressions:

a) log₃ (x²y)

b) ln((a√b)/c³)

4. Condense the following logarithmic expressions into a single logarithm:

a) 2 log x + 3 log y

b) ½ ln(x) - 4 ln(y) + ln(z)

5. Which of the following is the solution to the equation log₅(2x - 1) = 2?

6. Solve the following logarithmic equations:

a) log(x + 2) + log(x - 1) = 1

b) ln(3x) = ln(x - 2) + ln(4)