Question

True or False? If x>0 and a>1, then (ln x/ln a) = ln (x/a) Counter example if false.

Answer 1

it should be \[\ln (x)/\ln (y)=\log_{y}x \]

Answer 2

false
what if a=e and x=1
\[\frac{\ln(1)}{\ln(e)}=\frac{0}{1}=0 \neq -1=(-1)\ln(e)=\ln(e^{-1})=\ln(\frac{1}{e})\]

Answer 3

you are a genius.