Algebra 2

$f(g(7))\quad =\quad { e }^{ 2\ln { 7 } }={ e }^{ \ln { ({ 7 }^{ 2 }) } }={ e }^{ \ln { 49 } }=49$

${ e }^{ 2\ln { 7 } }={ e }^{ \ln { ({ 7 }^{ 2 }) } }$ because you can move the number in front of the natural log to the exponent above the argument (power rule).

${ e }^{ \ln { 49 } }=49$ because the e raised to the natural log of any number is that number