Logarithms: Change of Base Formula Worksheet
This worksheet focuses on applying the change of base formula for logarithms, including evaluating expressions and solving equations.
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Logarithms: Change of Base Formula
Name:
Date:
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Read each question carefully and use the change of base formula to solve. Round your answers to four decimal places where necessary.
1. The Change of Base Formula states that log_b(a) = log_c(a) / .
2. When using a calculator, it is often easiest to change the base to either 10 (common logarithm) or (natural logarithm).
3. If log_x(y) = 3 and log_y(z) = 2, then log_x(z) = .
4. Which of the following is equivalent to log_3(7)?
ln(7) / ln(3)
log(3) / log(7)
log(7 - 3)
log(7) * log(3)
5. Evaluate log_5(100) to four decimal places.
0.3010
2.8614
1.6990
2.0000
6. Use the change of base formula to express log_2(15) in terms of the natural logarithm (ln). Then, evaluate your expression to four decimal places.
7. Solve for x: log_x(64) = 3. Use the change of base formula as part of your solution process.
8. Given log_a(b) = 2.5 and log_c(b) = 1.2, find log_a(c). Show your work.
9. log_b(a) = log(a) - log(b) is a correct application of the change of base formula.
True
False
10. The change of base formula allows us to convert a logarithm of any base to a logarithm of base 10 or base e.
True
False
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