Question

The answer is not .5

Simplify mentally using the properties of logarithms. Give answers as reduced fractions where appropriate. In(Ve) Preview Enter a fraction or integer (no mixed numbers) [more.) Points possible: 1 This is attempt 2 of 2. Message instructor about this question Submit

Answer 1

NOTE: Answer will be accepted as 1/2 not 0.5 for ur website

Given is-
$\small \ln \left(\sqrt{e}\right)$

This can be rewritten as
$\small =>\ln \left(\sqrt{e}\right)=\ln \left(e^{\frac{1}{2}}\right)$

Apply log rule- $\small \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)$
$\small =>\ln \left(e^{\frac{1}{2}}\right)=\frac{1}{2}\ln \left(e\right)$

Apply log rule- $\small \log _a\left(a\right)=1$
$\small =>\frac{1}{2}\ln \left(e\right)=\frac{1}{2}(1)$

So we have $\small \bullet \ \small \ln \left(\sqrt{e}\right)=\frac{1}{2}$