Expanding and Condensing Logarithms Worksheet with Answer Key

What's on the worksheet

1. Expand each logarithm fully and evaluate any logarithm of a number.
   \log_6 \dfrac{a^2 b^5}{36}\ln \dfrac{\sqrt[5]{x^2}}{e^4 y}\log\left(x^3\sqrt{1000y}\right)\log_2 \left(\dfrac{4\sqrt{x}}{y}\right)^{3}\log_3 \sqrt[3]{x^2\sqrt{x}}
2. Write each expression as a single logarithm with coefficient 1.
   2 - 3\log_3 m\dfrac{1}{4}\left(3\ln p - \ln q\right) + \ln r3\left(\log_2 u - 2\log_2 v\right) - \log_2 w\dfrac{1}{2}\ln x + \dfrac{1}{3}\ln x
3. Factor and expand a logarithm of a rational expression and find where it holds.
4. Test the laws of logs at negative inputs for x and y.
5. Show each expression has the same value for every positive x and find that value.
6. Find the error in each of Layla's three lines.