# Find the exact value of the logarithmic expression \ln\left(\frac{1}{\sqrt e}

Find the exact value of the logarithmic expression $\mathrm{ln}\left(\frac{1}{\sqrt{e}}\right)$ without using a calculator.If this is not possible, state the reason.
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Faiza Fuller
Step 1
Given:
Let $y=\mathrm{ln}\left(\frac{1}{\sqrt{e}}\right)$
To Find: To evaluate the given expression.
Step 2
Solution:
$y=\mathrm{ln}\left(\frac{1}{\sqrt{e}}\right)$

$⇒y=\mathrm{ln}1-\mathrm{ln}\left(\sqrt{e}\right)$

$⇒y=0-\mathrm{ln}\left(\sqrt{e}\right)$
$y=-{\mathrm{ln}\left(e\right)}^{\frac{1}{2}}$

$⇒y=-\frac{1}{2}\mathrm{ln}e$

$⇒y=-\frac{1}{2}×1$
$y=\frac{-1}{2}$