Chapter 10: Q. 10.74 (page 1043)

Rounding to three decimal places, approximate $\log_{5} 46 .$

Short Answer

Expert verified

By rounding to three decimal places, the approximation of the logarithm is $2.379 .$

Step by step solution

Step 1. Given Information

The given logarithm is $\log_{5} 46 .$

We have to round it to three decimal places and approximate the result.

Step 2. Use the Change-of-Base Formula

To evaluate a logarithm with any other base, we can use the Change-of-Base Formula.

The Change-of-base formula is

$\log_{a} M = \frac{\log_{b} M}{\log_{b} a} .$

Thus, we will take 10 as b

$\log_{5} 46 = \frac{\log_{10} 46}{\log_{10} 5} .$

Step 3. Use the calculator

To find the approximate value of the logarithm use the calculator and enter the expression.

So, we use the log button for base 10 in the calculator.

We get $\frac{\log_{10} 46}{\log_{10} 5} \approx 2.379 .$

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Rounding to three decimal places, approximate $\log_{5} 46 .$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Use the Change-of-Base Formula

Step 3. Use the calculator

One App. One Place for Learning.

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Rounding to three decimal places, approximatelog546.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Use the Change-of-Base Formula

Step 3. Use the calculator

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Geometry

Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Rounding to three decimal places, approximate $\log_{5} 46 .$