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Change of base formula worksheets Grade 11

Evaluate logarithms by changing to a convenient base.

The front of the free change of base formula worksheet
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Free · Worked example · 46 problems · Answer key · US Letter

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How to do it

log base a of y = (log y) ÷ (log a), in any base. Choose a base that makes both easy.

log⁡816=log⁡216log⁡28=43\log_{8} 16 = \dfrac{\log_{2} 16}{\log_{2} 8} = \dfrac{4}{3}change of base: both 16 and 8 are powers of 2

Example problems

  1. log⁡816=\log_{8} 16 =
  2. log⁡832=\log_{8} 32 =
  3. log⁡42=\log_{4} 2 =
  4. log⁡12525=\log_{125} 25 =

Exponential and logarithmic functions

  1. Solving exponential equations with a common base
  2. Evaluating logarithms
  3. Solving logarithmic equations with the definition
  4. Logarithm rules with numbers
  5. Expanding and condensing logarithms
  6. Change of base formula
  7. Solving exponential equations with logarithms
  8. Solving logarithmic equations
  9. Exponential growth and decay