Logarithm Rules Practice Worksheet
Practice applying the fundamental rules of logarithms, including product, quotient, power, and change of base rules.
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Logarithm Rules Practice
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Read each question carefully and apply the appropriate logarithm rule to solve. Show all your work for full credit.
1. The Product Rule states that log_b(MN) = .
2. The Quotient Rule states that log_b(M/N) = .
3. The Power Rule states that log_b(M^p) = .
4. The Change of Base Formula allows us to write log_b(M) as .
Expand the following logarithmic expressions:
5. log_2(8xy)
6. log_3(x^5 / y^2)
7. ln(√(ab))
Condense the following logarithmic expressions into a single logarithm:
8. log(x) + log(y) - log(z)
9. 3ln(a) + 2ln(b)
10. (1/2)log_5(x) - 4log_5(y)
11. Which expression is equivalent to log_b(x^3 * y)?
3log_b(x) + log_b(y)
log_b(3x) + log_b(y)
log_b(x^3) * log_b(y)
log_b(x) + 3log_b(y)
12. If log_10(5) ≈ 0.699 and log_10(2) ≈ 0.301, what is log_10(100)?
0.301
0.699
1
2
13. Given log_a(x) = 2 and log_a(y) = 3, find log_a(x^2 * y^3 / a).