Question

please solve step by step and send photo

Answer 1

Given, $\bold{(2^{log_6^{18}}).(3^{log_6^3})}$
Let y = $\bold{(2^{log_6^{18}}).(3^{log_6^3})}$
Taking log both sides with base 6
$\bold{log_6^y=log_6^{(2^{log_6^{18}}).(3^{log_6^3})}}$
$\bold{log_6^y= log_6^{18}log_6^2+log_6^3log_6^3}$
$\bold{log_6^y= log_6^{6\times 3}log_6^2+log_6^3log_6^3}$
$\bold{log_6^y= (log_6^6+log_6^3)log_6^2+log_6^3log_6^3}$
$\bold{log_6^y= (1+log_6^3)log_6^2+log_6^3log_6^3}$
$\bold{log_6^y= log_6^2+log_6^3(log_6^2+log_6^3)}$
$\bold{log_6^y= log_6^2+log_6^3.log_6^{3\times2}}$
$\bold{log_6^y= log_6^2+log_6^3.log_6^6}\\\bold{log_6^y=log_6^2+log_6^3.1}\\\bold{log_6^y=log_6^{3\times2}}\\\bold{log_6^y=log_6^6}\\\bold{log_6^y=1}\\\\\boxed{\boxed{\bold{y=6}}}$

Answer 2

here is ur answer

i hope it helps u