Answer
(a) ln$e^{sinx}=sinx$
(b) $e^{x+lnx}=xe^{x}$
Work Step by Step
The exponential function is defined by if $e^{x}=y$ then $x =lny$.
(a) ln$e^{sinx}=sinx$
(b) $e^{x+lnx}=e^{x}\times e^{lnx}$
$=e^{x}x$
Hence,
$e^{x+lnx}=xe^{x}$