Question

Evaluating Logarithms Evaluate the expression.

(a)$e^{\ln \sqrt{3}}$ (b) $e^{\ln \left(1/\pi \right)}$ (c)${10}^{\log 13}$

Short answer

1. The required value is $\sqrt{3}$.
2. The required value is$\frac{1}{\pi }$.
3. The required value is 13.

Step-by-step solution

Part a. Step 1. Given.

The given expression is $e^{\ln \sqrt{3}}$.

Part a. Step 2. To determine.

We have to evaluate the given expression.

Part a. Step 3. Calculation.

We’ll use the formula: $e^{\ln b}=b$.

We compare$e^{\ln \sqrt{3}}$ with $e^{\ln b}$. So, $b=\sqrt{3}$.

Hence, $e^{\ln \sqrt{3}}=b=\sqrt{3}$.

Part b. Step 1. Given.

The given exponential form is $e^{\ln \left(1/\pi \right)}$.

Part b. Step 2. To determine.

We have to evaluate the given expression.

Part b. Step 3. Calculation.

We’ll use the formula: $e^{\ln b}=b$.

We compare$e^{\ln \left(1/\pi \right)}$ with $e^{\ln b}$. So, $b=\frac{1}{\pi }$.

Hence, $e^{\ln \left(1/\pi \right)}=b=\frac{1}{\pi }$.

Part c. Step 1. Given.

The given exponential form is ${10}^{\log 13}$.

Part c. Step 2. To determine.

We have to evaluate the given expression.

Part c. Step 3. Calculation.

We’ll use the formula: ${10}^{\log b}=b$.

We compare${10}^{\log 13}$ with ${10}^{\log b}$. So, $b=13$.

Hence, ${10}^{\log 13}=b=13$.