We are asked to simplify the expression $\log(\frac{1}{\sqrt{x}})$. We will assume the logarithm is base 10.

1. Problem Description

We are asked to simplify the expression $\log(\frac{1}{\sqrt{x}})$. We will assume the logarithm is base

1

0.

2. Solution Steps

First, we can rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$. Therefore, $\frac{1}{\sqrt{x}}$ can be rewritten as $\frac{1}{x^{\frac{1}{2}}} = x^{-\frac{1}{2}}$.

So we have $\log(x^{-\frac{1}{2}})$.

Using the logarithm power rule, which states that $\log(a^b) = b \log(a)$, we can rewrite $\log(x^{-\frac{1}{2}})$ as $-\frac{1}{2} \log(x)$.

3. Final Answer

The simplified expression is $-\frac{1}{2} \log(x)$.