Question

Use the properties of logarithms and the values below to find the logarithm indicated. Do not use a calculator to evaluate the logs.

1. \[\log_{8}6 \approx0.9\]
\[\log_{8}5\approx0.8 \]
\[\log_{8}9\approx1.1 \]
Find \[\log_{8} \frac{ 1 }{ 36 }\]

Answer 1

Use the properties of logarithms and the values below to find the logarithm indicated. Do not use a calculator to evaluate the logs.

1. \[\log_{8}6 \approx0.9\]
\[\log_{8}5\approx0.8 \]
\[\log_{8}9\approx1.1 \]
Find \[\log_{8} \frac{ 1 }{ 36 }\]

Answer 2

well take the question are rewrite it

\[\log_{8} \frac{1}{36} = \log_{8}\frac{1}{6^2}\]

the log laws for division says subtract the logs

\[\log_{8}\frac{1}{6^2} = \log_{8}(1) - \log_{8}(6^2)\]

you now need to use the power law for logs

\[\log_{8}(1) - 2 \times \log_{8} (6)\]

just evaluate it... and I hope it helps

Answer 3

Thanks!