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

6-28.

Since $y=e^x$ and $y =\operatorname{ln}(x)$ are inverse functions, $e^{\operatorname{ln}(x)}=x$ and $\operatorname{ln}(e^x)=x$. Use these facts along with exponent and log laws to rewrite each expression.

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

$e^{2\operatorname{ln}x}=e^{\operatorname{ln}x2}$

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

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

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

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