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

Step 1. Given information.

Consider the given information.

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

Step 2. Calculation.

Apply the properties of logarithms.

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

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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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

Step by step solution

Step 1. Given information.

Step 2. Calculation.

Step 3. Substitute the given values.

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Suppose that ln 2 = a and ln 3 = b. Use properties of logarithms to write each logarithm in terms of a and b.ln234

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

Step 3. Substitute the given values.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

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