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Properties of Logarithms (Algebra 2)

Free printable Algebra 2 worksheet on the product, quotient and power rules of logarithms: expanding, condensing, and evaluating logarithms of perfect powers.

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Algebra 2 Ā· Math worksheet
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Algebra 2: Properties of Logarithms

Assume every variable is positive. Use the product, quotient and power rules to expand or condense each expression, or evaluate the logarithm exactly.

  1. 1.
    Expand as a sum or difference of logarithms: logā‚‚(y4y^{4}z)
  2. 2.
    Expand as a sum or difference of logarithms: logā‚…(x3x^{3}/y)
  3. 3.
    Expand as a sum or difference of logarithms: logā‚…(y3y^{3}z)
  4. 4.
    Expand as a sum or difference of logarithms: logā‚…(y3y^{3}/z)
  5. 5.
    Write as a single logarithm: 3logā‚‚(x) + logā‚‚(z)
  6. 6.
    Write as a single logarithm: 3logā‚ƒ(y) - logā‚ƒ(z)
  7. 7.
    Write as a single logarithm: 3logā‚ƒ(x) + logā‚ƒ(y)
  8. 8.
    Write as a single logarithm: 3log(y) - log(z)
  9. 9.
    Evaluate: logā‚ƒ(13)
  10. 10.
    Evaluate: logā‚…(15)
  11. 11.
    Evaluate: log(100)
  12. 12.
    Evaluate: logā‚…(125)
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