QuestionJuly 15, 2025

Simplify the logarithmic expression. Express powers as factors. log_(3)z^6 log_(3)z^6= square (Type an exact answer in simplified form.)

Simplify the logarithmic expression. Express powers as factors. log_(3)z^6 log_(3)z^6= square (Type an exact answer in simplified form.)
Simplify the logarithmic expression. Express powers as factors.
log_(3)z^6
log_(3)z^6= square  (Type an exact answer in simplified form.)

Solution
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Answer

6 \cdot \log_{3}(z) Explanation 1. Apply the Power Rule of Logarithms Use the power rule: ** \log_b(x^n) = n \cdot \log_b(x) **. Here, n = 6 and x = z. Therefore, \log_{3}(z^6) = 6 \cdot \log_{3}(z) .

Explanation

1. Apply the Power Rule of Logarithms<br /> Use the power rule: **$ \log_b(x^n) = n \cdot \log_b(x) $**. Here, $n = 6$ and $x = z$.<br /> Therefore, $ \log_{3}(z^6) = 6 \cdot \log_{3}(z) $.
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