Chapter 5: Q 35. (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.
$\ln \sqrt[5]{6}$

Short Answer

Expert verified

The result is $\frac{1}{5} (a + b)$ .

Step by step solution

Step 1. Given information.

Consider the given information.

$\ln \sqrt[5]{6}$

Step 2. Calculation.

Apply the properties of logarithms.

$\begin{array}{l} \ln \sqrt[5]{6} = \ln 6^{\frac{1}{5}} \\ = \frac{1}{5} \ln (2 \cdot 3) \\ = \frac{1}{5} [\ln 2 + \ln 3] \end{array}$

Step 3. Substitute the given values.

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

$\frac{1}{5} [\ln 2 + \ln 3] = \frac{1}{5} (a + b)$

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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.
$\ln \sqrt[5]{6}$

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.ln65

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

Statistics

Theoretical and Mathematical Physics

Probability and Statistics

Pure Maths

Mechanics Maths

Discrete Mathematics

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.
$\ln \sqrt[5]{6}$