Evaluating Logarithms, Common and Natural Worksheet with Answer Key

What's on the worksheet

1. Evaluate each logarithm without a calculator.
   \log_{17} 1\log_2 \dfrac{1}{32}\log_4 0.25\log_{1/5} \dfrac{1}{625}\log_{0.1} 1000
2. Evaluate by writing the base and argument as powers of one smaller base.
   \log_{16} 8\log_{1/8} \dfrac{1}{16}\log_4 \sqrt[3]{2}\log_{\sqrt[3]{5}} 25\log_8 \dfrac{1}{\sqrt{2}}
3. Evaluate exactly with common and natural logarithms.
   \ln 1\log \dfrac{1}{\sqrt{10}}\log \left(100\sqrt[3]{10}\right)\ln \left(e^2\sqrt{e}\right)\ln \dfrac{1}{e^{-3}}
4. Find the two integers each logarithm lies between and list all six from least to greatest.
5. Say whether each value is positive, negative, zero or not a real number, with a reason.
   \log_7 0.9\log 1.001\log_{2/5} 1\log_{0.5} 6\log_{0.3} 0.2
6. Explain the error in each line of Mateo's work and give the correct value.
7. Find every whole-number base for which the log of 64 is a whole number, and explain why others fail.