Logarithmic Function Manipulation Worksheet
Practice manipulating and evaluating logarithmic functions, including applying properties of logarithms and solving logarithmic equations.
Includes
Standards
Logarithmic Function Manipulation
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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?
x = 3
x = 8
x = 13
x = 26
6. Solve the following logarithmic equations:
a) log(x + 2) + log(x - 1) = 1
b) ln(3x) = ln(x - 2) + ln(4)