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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q 13. (page 308)

use properties of logarithms to find the exact value of each expression. Do not use a calculator.
$\log_{3} 3^{71}$

Short Answer

Expert verified

The value is 71.

Step by step solution

01

Step 1. Given information.

Consider the given information.

$\log_{3} 3^{71}$

02

Step 2. Logarithm properties.

The properties are defined as,

$\begin{array}{l} \log_{a} a = 1 \\ \log (M N) = \log_{a} M + \log_{a} N \\ \log_{a} (\frac{M}{N}) = \log_{a} M - \log_{a} N \\ \log_{a} M^{r} = r \log_{a} M \end{array}$

03

Step 3. Calculation.

Apply the properties.

$\begin{array}{rcl} \log_{3} 3^{71} & = & 71 \log_{3} 3 \\ = & 71 (1) \\ = & 71 \end{array}$

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