Definition of a Logarithm Worksheet with Answer Key

What's on the worksheet

1. Write each statement in exponential form.
   \log_{\frac{1}{3}} 27 = -3\log 0.0001 = -4\ln \sqrt{e} = \dfrac{1}{2}\log_a c = k
2. Write each statement in logarithmic form.
   \left(\dfrac{2}{5}\right)^{-2} = \dfrac{25}{4}81^{\frac{3}{4}} = 27e^{-0.4} = p\sqrt[3]{64} = 4
3. Solve each equation by writing it in exponential form, with exact answers.
   \log_{\frac{1}{2}} x = -3\log x = \dfrac{1}{3}\log_b 1000 = \dfrac{3}{2}\log_b 8 = -3
4. Solve an exponential equation exactly using a logarithm and place the answer between whole numbers.
5. Solve each log equation and check for an allowed base and a positive argument.
6. Find the inverse of a log function, with its domain and range.
7. Find which numbers Leah put in the wrong places when solving a log equation.