Question

Why does ln(1/3)/ln(3) = -1? What's the logarithm rule for this?

Answer 1

or \[\ln a^b=b \ln a\]
\[\ln(\frac13)/\ln3=\ln3^{-1}/\ln3=-1*\ln3/\ln3=-1\]

Answer 2

\[\frac{\log(\frac{1}{3})}{\log(3)}=\frac{\log(1)-\log(3)}{\log(3)}=\frac{0-\log(3)}{\log(3)}=-1\]

Answer 3

cinar's method is also correct