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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 36. (page 308)

Suppose that ln 2 = a and ln 3 = b. Use properties of logarithms to write each logarithm in terms of a and b.
$\ln \sqrt[4]{\frac{2}{3}}$

Short Answer

Expert verified

The result is $\frac{1}{4} (a + b)$ .

Step by step solution

01

Step 1. Given information.

Consider the given information.

$\ln \sqrt[4]{\frac{2}{3}}$

02

Step 2. Calculation.

Apply the properties of logarithms.

$\begin{array}{l} \ln \sqrt[4]{\frac{2}{3}} = \ln {(\frac{2}{3})}^{\frac{1}{4}} \\ = \frac{1}{4} \ln (\frac{2}{3}) \\ = \frac{1}{4} [\ln 2 + \ln 3] \end{array}$

03

Step 3. Substitute the given values.

Substitute ln 2 = a and ln 3 = bin the obtained result.

$\frac{1}{4} [\ln 2 + \ln 3] = \frac{1}{4} (a + b)$

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