Change of Base Worksheet with Answer Key

What's on the worksheet

1. Use change of base: give the two integers each logarithm lies between and its value to four decimal places.
   \log_6 200\log_{13} 2{,}000\log_{15} 0.02\log_{0.6} 0.05
2. Find each exact value by writing the logarithms over one convenient base.
   \dfrac{\log_5 8}{\log_5 2}\log_2 5 \cdot \log_{25} 16\log_8 3 \cdot \log_9 32\log_{\sqrt{2}} 3 \cdot \log_{27} 4
3. Check Leah's change of base calculation for the logarithm of 300 in base 7.
4. Write each logarithm in terms of p, where p is a base 2 logarithm of x.
5. Find the whole number bases for which a logarithm of 50 lies between 2 and 3.
6. Find the base whose logarithm graph is one third the height of the base 2 graph.
7. Show a relationship between logarithms in different bases, for allowed bases a and b.