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Logarithm rules with numbers worksheets Grade 11

Combine logs with the product and quotient rules, then evaluate.

The front of the free logarithm rules with numbers worksheet
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Free · Worked example · 40 problems · Answer key · US Letter

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How to do it

log a + log b = log(ab). log a − log b = log(a ÷ b). Use the same base. Then evaluate.

log⁡3108−log⁡34=log⁡31084=log⁡327=3\log_{3} 108 - \log_{3} 4 = \log_{3} \dfrac{108}{4} = \log_{3} 27 = 3subtracting logs: divide inside

Example problems

  1. log⁡6144−log⁡64=\log_{6} 144 - \log_{6} 4 =
  2. log⁡24+log⁡24=\log_{2} 4 + \log_{2} 4 =
  3. log⁡6108−log⁡63=\log_{6} 108 - \log_{6} 3 =
  4. log⁡264−log⁡28=\log_{2} 64 - \log_{2} 8 =

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