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Chapter 13: Problem 18

Write as the sum or difference of logarithms and simplify, if possible. Assume all variables represent positive real numbers. $$\log _{3} z^{5}$$

Short Answer

Expert verified
The simplified expression for \(\log_{3} z^{5}\) is \(5\log_{3} z\).

Step by step solution

01

Apply the power rule of logarithms

The power rule of logarithms states that \(\log_{a}(x^p) = p\log_{a}(x)\). We can apply this rule to our given expression, which is \(\log _{3} z^{5}\). We have a base of 3 and an exponent of 5. Therefore, we get: \[ 5\log _{3} z \]
02

Simplify the expression

Since there are no further opportunities to rewrite \(\log _{3} z\) as a sum or difference, we have simplified the expression to its final form. The simplified expression is: \[ 5\log_{3} z \]

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