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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 283 (page 1045)

In the following exercises, use the Change-of-Base Formula, rounding to three decimal places, to approximate each logarithm.
$\log_{\sqrt{3}} 21$

Short Answer

Expert verified

The answer is $5.542$

Step by step solution

01

Step 1. Given information

The given logarithmic expression is $\log_{\sqrt{3}} 21$

02

Step 2. Calculate the value

Use the change of base formula that is $\log_{a} M = \frac{\log_{b} M}{\log_{b} a}$

So,

$\log_{\sqrt{3}} 21 = \frac{\log_{10} 21}{\log_{10} \sqrt{3}} = 5.542$

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Most popular questions from this chapter

In the following exercises, solve each logarithmic equation.

$y = \log_{\frac{1}{3}} (x)$

Convert from exponential to logarithmic form:

$10^{- 2} = \frac{1}{100}$ .

In the following exercises, graph, on the same coordinate system, the inverse of the one-to-one function shown.

On the same coordinate system, graph:

$f (x) = 3^{x}$

$g (x) = 3^{x + 1}$

Graph: $g (x) = 5^{x}$

See all solutions

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