### Home > APCALC > Chapter 6 > Lesson 6.1.2 > Problem6-28

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.

1. $\quad e ^ { 2 \operatorname { ln } ( x ) }$

$e^{2\ln x}=e^{\ln x^2}$

1. $\quad e ^ { \operatorname { ln } \sqrt { x } }$

$\sqrt{x}$

1. $\operatorname { ln } \sqrt { e ^ { 5 x } }$

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

1.  $\operatorname { ln } ( 5 e ^ { x } )$

$\ln\left(5e^x\right)=\ln\left(e^{\ln5}e^x\right)$