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Expanding and condensing logarithms worksheets Grade 11

Expand logs with the product, quotient and power rules, or condense them into one log.

The front of the free expanding and condensing logarithms worksheet
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Free · Worked example · 34 problems · Answer key · US Letter

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How to do it

Product: add logs. Quotient: subtract logs. Power: the exponent moves to the front. To condense, go the other way.

4log⁡2x+log⁡24=log⁡2x4+log⁡24=log⁡2(4x4)4 \log_{2} x + \log_{2} 4 = \log_{2} x^{4} + \log_{2} 4 = \log_{2} (4x^{4})move 4 up as a power, then multiply inside

Example problems

  1. log⁡2(4x2)=\log_{2} (4x^{2}) =
  2. log⁡3x327=\log_{3} \dfrac{x^{3}}{27} =
  3. 5log⁡5x+log⁡54=5 \log_{5} x + \log_{5} 4 =
  4. log⁡3(27x3)=\log_{3} (27x^{3}) =

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