Logarithm Laws Worksheet
Grade 12 Math worksheet focusing on the application of logarithm laws for simplification and solving equations.
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Logarithm Laws Worksheet
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Read each question carefully and apply the appropriate logarithm laws to solve or simplify the expressions. Show all your work.
1. Simplify the following expression: log(x) + log(y) - log(z)
2. Express 3log(a) + 2log(b) as a single logarithm.
3. Simplify: log₂(8) + log₂(4)
4. Which of the following is equivalent to log(x^n)?
n + log(x)
log(x) / n
n * log(x)
log(n * x)
5. Given log₅(2) ≈ 0.43 and log₅(3) ≈ 0.68, what is log₅(6)?
0.29
1.11
0.25
2.04
6. The product rule of logarithms states that logₐ(MN) = .
7. The quotient rule of logarithms states that logₐ(M/N) = .
8. The power rule of logarithms states that logₐ(Mᵖ) = .
Match each logarithm expression with the correct equivalent expression.
9. log(A) + log(B)
a. log(A/B)
10. log(A) - log(B)
b. log(A * B)
11. log(A^C)
c. C * log(A)
12. Solve for x: log₃(x) + log₃(4) = log₃(20)
13. Solve for x: log(x + 2) - log(x) = log(3)