Problem

Use the power property to rewrite each expression. Assume all variables are positive. \[ \log _{3}\left(a^{-3}\right)= \] The answer format in lowercase characters is: $\log _{-}$base (number) Spaces in the answer are optional.

Solution

Step 1 :Use the power property of logarithms which states that \(\log_b(a^n) = n \cdot \log_b(a)\).

Step 2 :Apply this property to the given expression \(\log_3(a^{-3})\) to rewrite it as \(-3 \cdot \log_3(a)\).

Step 3 :The rewritten expression using the power property of logarithms is \(\boxed{-3 \cdot \log_3(a)}\).

From Solvely APP
Source: https://solvelyapp.com/problems/31427/

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