Question

In the following exercises, use the properties of logarithms to evaluate.
(a)${10}^{\log \sqrt{5}}$

(b)$\log {\left(10\right)}^{-3}$

Short answer

The solution is-

(a)$\sqrt{5}$

(b)$-3$

Step-by-step solution

Step 1. Solving for part (a)

We have${10}^{\log \sqrt{5}}$.
This can be written as${10}^{{\log }_{10}\sqrt{5}}$.

We will evaluate this using the property, $a^{{\log }_{a}x}=x$. So,

${10}^{{\log }_{10}\sqrt{5}}=\sqrt{5}$.

Step 2. Solving for part (b)

We have$\log {\left(10\right)}^{-3}$.
This can be written as${\log }_{10}{\left(10\right)}^{-3}$

We will evaluate this using the property, ${\log }_a{a}^x=x$. So,

${\log }_{10}{\left(10\right)}^{-3}=-3$.