Change of Base Formula Worksheet
Understand and apply the change of base formula for logarithms with this Grade 9 math worksheet.
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Change of Base Formula Practice
Name:
Date:
Score:
Read each question carefully and use the change of base formula to solve. Round your answers to two decimal places where necessary.
1. The change of base formula states that log_b(a) = / log_c(b).
2. When using a calculator that only has log base 10 or natural log (ln), the change of base formula is essential for evaluating logarithms with a base.
3. Which of the following is equivalent to log_3(7) using the change of base formula?
log(3) / log(7)
log(7) / log(3)
log_7(3)
log(10) / log(7)
4. If log_x(y) = 5 and log_x(z) = 2, what is log_z(y)?
2.5
0.4
10
7
5. Evaluate log_2(10) using the change of base formula and common logarithms (log base 10). Show your work.
6. Evaluate log_5(100) using the change of base formula and natural logarithms (ln). Show your work.
7. The change of base formula can only be used with common logarithms (log base 10).
True
False
8. log_a(b) = 1 / log_b(a) is a direct consequence of the change of base formula.
True
False
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