## anonymous 5 years ago how do you simplify ln square root e, and is the answer e^2?

1. anonymous

no it is $\frac{1}{2}$

2. anonymous

$ln(x)=y$ same as $e^y=x$ $ln(\sqrt{e})=ln(e^{\frac{1}{2}})$

3. anonymous

this is starting to make a lot more sense thanx a lot!

4. anonymous

and since clearly $e^{y}=e^{\frac{1}{2}}$ makes $y=\frac{1}{2}$ we get $ln(e^{\frac{1}{2}})=\frac{1}{2}$

5. anonymous

this of it this way. $ln(x)$ is the power you raise e to to get x. therefore $ln(e^y)=y$

6. anonymous

just like $log_3(3^2)=2$

7. anonymous

and $log_{10}(.001)=-3$ since $10^{-3}=.001$

8. anonymous

10 ^-4 = 0.0001?

9. anonymous

yes, since $10^{-4}=\frac{1}{10^4}=\frac{1}{10000}=.0001$