Question

if log of 2 to the base 10=.301
log of 25 to the base 8=?
show how to solve

Answer 1

\[\log_{10} 2 = .301 \]
\[\log_{8} 25 = \frac{\log 25}{\log 8} = \frac{1.398}{.903} = 1.548 \]
Basically use change of base formula
\[\log_{b} x = \frac{\log x}{\log b} \]

Answer 2

hah! you can't do that?

Answer 3

\[\log_{8}25=2\log_{10}5/3\log_{10}2=2(1-\log_{10}2)/3\log_{10}2=2*(1-.301)/(3*.301)=1.548 \]

Answer 4

very nice :)