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

Step 1. Given information.

Consider the given information.

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

Step 2. Logarithm properties.

The properties are defined as,

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

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Logarithm properties.

Step 3. Calculation.

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use properties of logarithms to find the exact value of each expression. Do not use a calculator.log3371

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Logarithm properties.

Step 3. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Mechanics Maths

Theoretical and Mathematical Physics

Geometry

Pure Maths

Study anywhere. Anytime. Across all devices.

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