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Chapter 13: Problem 39

Write as the sum or difference of logarithms and simplify, if possible. Assume all variables represent positive real numbers. $$\log \frac{\sqrt[5]{11}}{y^{2}}$$

Short Answer

Expert verified
\( \frac{1}{5}\log(11) - 2\log(y) \)

Step by step solution

01

Apply the quotient rule of logarithms

We apply the quotient rule to the given logarithm expression: $$\log \frac{\sqrt[5]{11}}{y^{2}} = \log(\sqrt[5]{11}) - \log(y^{2})$$
02

Rewrite the fifth root

The fifth root can be written as a fractional exponent, like this: $$\sqrt[5]{11} = 11^{\frac{1}{5}}$$ Now the expression becomes: $$\log(11^{\frac{1}{5}}) - \log(y^{2})$$
03

Apply the power rule of logarithms

We apply the power rule to both logarithm expressions: $$\frac{1}{5}\log(11) - 2\log(y)$$ Now, we have the expression written as the sum or difference of logarithms simplified as much as possible: $$\frac{1}{5}\log(11) - 2\log(y)$$

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Most popular questions from this chapter

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