Question: Find the logarithm using the change of base formula. \(\log_{8} 0.08\)

Find the logarithm using the change of base formula.

\(\log_{8} 0.08\)

Solution

To find the logarithm using the change of base formula. \[ \log_8 0.08 = \frac{\log 0.08}{\log 8} \] Calculate the logarithms. \[ \log 0.08 \approx -1.09691 \] \[ \log 8 \approx 0.90309 \] Divide the two. \[ \frac{-1.09691}{0.90309} \approx -1.212 \] Therefore, \[ \log_8 0.08 \approx -1.212 \]