CPM Homework Help : CALC3RD Problem 6-28

Since $y = e^x$ and $y = \ln(x)$ are inverse functions, $e^{ln(x)} = x$ and $\ln(e^x) = x$ . Use these facts along with properties of exponents and logarithms to rewrite each expression.

$\quad e ^ { 2 \operatorname { ln } ( x ) }$
Hint (a):
$e^{2\ln x}=e^{\ln x^2}$

$\quad e ^ { \operatorname { ln } \sqrt { x } }$
Answer (b):
$\sqrt{x}$

$\operatorname { ln } \sqrt { e ^ { 5 x } }$
Hint (c):
$\text{ln}\sqrt{\text{e}^{5x}}=\text{ln}\left ( \text{e}^{\frac{5}{2}x} \right )$

$\operatorname { ln } ( 5 e ^ { x } )$
Hint (d):
$\ln\left(5e^x\right)=\ln\left(e^{\ln5}e^x\right)$