Question

Use the change of base formula to evaluate each to three decimal places.
log(8)105

Answer 1

Do you know the change of base formula and where it comes from? if we rewrite this as an exponential
\[\log_{8}105\rightarrow 8^{x}=105\].
Now take the logarithm of both sides in base 10 or e:
\[\ln \left( 8^{x} \right)=\ln \left( 105 \right)\rightarrow xln\left( 8 \right)=\ln \left( 105 \right) \rightarrow x=\frac{ \ln \left( 105 \right) }{ \ln\left( 8 \right) }\] You can use a calculator to compute these.

Answer 2

so then it would be 2.238?

Answer 3

\[x=\ln _{8}105\]

Answer 4

oops, I mean \[x=\log_{8} 105\]
This is 2.238... you did great!