Find g(f(x)) f(x) = natural log of x , g(x)=e^(5x)

$f (x) = \ln (x)$ , $g (x) = e^{5 x}$

Set up the composite result function.

$g (f (x))$

Evaluate $g (f (x))$ by substituting in the value of $f$ into $g$ .

$e^{5 (\ln (x))}$

Simplify $5 (\ln (x))$ by moving $5$ inside the logarithm.

$g (\ln (x)) = e^{\ln (x^{5})}$

Exponentiation and log are inverse functions.

$g (\ln (x)) = x^{5}$

Find g(f(x)) f(x) = natural log of x , g(x)=e^(5x)

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