Question

The inverse of $y= 4^{ log_{e}x }$
(a) $x= y^{ log_{4}e }$ b)$x= y^{ log_{e}4 }$
c) $x= 4^{ log_{y}e }$ d) $x= 4^{ log_{e}y }$

Answer 1

$y = 4^{Log_e\ x}\\\\take\ logarithms\ to\ the\ base\ 4\\\\Log_4 y=Log_e x}\\\\x=e^{Log_4 y}$
There does not seem to be this option among the given options.

$Log_4 y=log_e x\\log_4 y=Log_4 x\ *\ Log_e 4\\\\ Log_4 x=\frac{1}{log_e 4}log_4 y\\\\=(log_4 e)*log_4\ y\\\\=Log_4\ (y^{log_4\ e})\\\\x=y^{log_4\ e}$

this is the option  (b)