How do you evaluate $ln \sqrt{e}$ $ln sqrt(e)$ ?

Question

39669 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-10T07:06:00

$\frac{1}{2}$ $1/2$

Recall that: $\sqrt{n} = n^{\frac{1}{2} :}$ $sqrtn=n^(1/2:$

We can now express your equation as:
$ln \sqrt{e} = {ln e}^{\frac{1}{2}}$ $lnsqrte=lne^(1/2)$

Recall that: ${log}_{n} a^{m} = m {log}_{n} a$ $log_na^m=mlog_na$

We can further simplify the given equation:

${ln e}^{\frac{1}{2}} = \frac{1}{2} ln e$ $lne^(1/2)=1/2lne$

Recall that: $ln e = {log}_{e} e = 1$ $lne=log_ee=1$

We can now say that:

$\frac{1}{2} ln e = \frac{1}{2} (1) = \frac{1}{2}$ $1/2lne=1/2(1)=1/2$

Therefore, $ln \sqrt{e} = \frac{1}{2}$ $lnsqrte=1/2$

How do you evaluate ln√eln sqrt(e)?