QuestionJuly 26, 2025

Condense into a single logarithm. Do not use fractional or negative exponents in your answer.You can type sqrt [n](m) as root(n)(m). (1)/(7)log_(8)(x)-12log_(8)(y)-11log_(8)(z) square

Condense into a single logarithm. Do not use fractional or negative exponents in your answer.You can type sqrt [n](m) as root(n)(m). (1)/(7)log_(8)(x)-12log_(8)(y)-11log_(8)(z) square
Condense into a single logarithm. Do not use fractional or negative exponents in your answer.You can type sqrt [n](m) as root(n)(m). (1)/(7)log_(8)(x)-12log_(8)(y)-11log_(8)(z) square

Solution
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Answer

\log_{8}(\frac{x^{\frac{1}{7}}}{y^{12}z^{11}}) Explanation 1. Apply Logarithm Power Rule Use the power rule: a \cdot \log_b(m) = \log_b(m^a) to rewrite each term. \frac{1}{7}\log_{8}(x) = \log_{8}(x^{\frac{1}{7}}), 12\log_{8}(y) = \log_{8}(y^{12}), 11\log_{8}(z) = \log_{8}(z^{11}). 2. Combine Using Logarithm Quotient Rule Use the quotient rule: \log_b(m) - \log_b(n) = \log_b(\frac{m}{n}). Combine into a single logarithm: \log_{8}(\frac{x^{\frac{1}{7}}}{y^{12}z^{11}}).

Explanation

1. Apply Logarithm Power Rule<br /> Use the power rule: $a \cdot \log_b(m) = \log_b(m^a)$ to rewrite each term.<br /> $\frac{1}{7}\log_{8}(x) = \log_{8}(x^{\frac{1}{7}})$, $12\log_{8}(y) = \log_{8}(y^{12})$, $11\log_{8}(z) = \log_{8}(z^{11})$.<br /><br />2. Combine Using Logarithm Quotient Rule<br /> Use the quotient rule: $\log_b(m) - \log_b(n) = \log_b(\frac{m}{n})$.<br /> Combine into a single logarithm: $\log_{8}(\frac{x^{\frac{1}{7}}}{y^{12}z^{11}})$.
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