logx to the base a * log y to the base b= logx to the base b * log y to the base a.please help

Question

hartnn · Answer

use this :
$\Large \log_xy = \dfrac{\log y}{\log x}$

mathmath333 · Answer

$\Large\rm    property~~~~\log_xy = \dfrac{\log_m y}{\log _m x}   $ 

$\Large\rm    \log_a  x \times   \log_b  y    $ 


$\Large\rm    =\dfrac{\log_b  x}{\log_b  a} \times  \dfrac{\log_a  y}{\log_a  b}     $


$\Large\rm    =\dfrac{\log_b  x\times \log_a  y }{\log_b  a \times \log_a  b }    $ 


$\Large\rm    =\log_b  x \times \log_a  y  $


 $\Large\rm   as~~ \log_b  a \times   \log_a  b=  \dfrac{\log_a  a}{\log_a  b } \times \log_a  b =\log_a  a=1$