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Q26.

Expert-verified
Found in: Page 352

### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

# Evaluating Logarithms Evaluate the expression.(a) ${\mathrm{log}}_{3}{3}^{7}$ (b) ${\mathrm{log}}_{4}64$ (c) ${\mathrm{log}}_{5}125$

1. The required value is 7.
2. The required value is 3.
3. The required value is 3.
See the step by step solution

## Part a. Step 1. Given.

The given exponential form is ${\mathrm{log}}_{3}{3}^{7}$.

## Part a. Step 2. To determine.

We have to evaluate the given expression.

## Part a. Step 3. Calculation.

We’ll use the formula: ${\mathrm{log}}_{a}\left({a}^{b}\right)=b$.

We will write ${\mathrm{log}}_{3}{3}^{7}$ in form ${\mathrm{log}}_{a}\left({a}^{b}\right)$ to find a and b. Then we’ll get the answer.

 Given ${\mathrm{log}}_{a}\left({a}^{b}\right)$ form a b Answer ${\mathrm{log}}_{3}{3}^{7}$ ${\mathrm{log}}_{3}\left({3}^{7}\right)$ 3 7 7

Hence, ${\mathrm{log}}_{3}{3}^{7}$ has value role="math" $=7$.

## Part b. Step 1. Given.

The given exponential form is ${\mathrm{log}}_{4}64$.

## Part b. Step 2. To determine.

We have to evaluate the given expression.

## Part b. Step 3. Calculation.

We’ll use the formula: ${\mathrm{log}}_{a}\left({a}^{b}\right)=b$.

We will write ${\mathrm{log}}_{4}64$ in form ${\mathrm{log}}_{a}\left({a}^{b}\right)$ to find a and b. Then we’ll get the answer.

 Given ${\mathrm{log}}_{a}\left({a}^{b}\right)$ form a b Answer ${\mathrm{log}}_{4}64$ ${\mathrm{log}}_{4}\left({4}^{3}\right)$ 4 3 3

Hence, ${\mathrm{log}}_{4}64$ has value $=3$.

## Part c. Step 1. Given.

The given exponential form is ${\mathrm{log}}_{5}125$.

## Part c. Step 2. To determine.

We have to evaluate the given expression.

## Part c. Step 3. Calculation.

We’ll use the formula: ${\mathrm{log}}_{a}\left({a}^{b}\right)=b$.

We will write ${\mathrm{log}}_{5}125$ in form ${\mathrm{log}}_{a}\left({a}^{b}\right)$ to find a and b. Then we’ll get the answer.

 Given ${\mathrm{log}}_{a}\left({a}^{b}\right)$ form a b Answer ${\mathrm{log}}_{5}125$ ${\mathrm{log}}_{5}\left({5}^{3}\right)$ 5 3 3

Hence, ${\mathrm{log}}_{5}125$ has value $=3$.