Math  /  Algebra

QuestionUse properties of logarithms to express each logarithm as a sum or difference logarithms. Assume that all variables represent positive real numbers. log3x4y5r4log3x4y5r4=\frac{\log _{3} \frac{\sqrt[4]{x} \cdot \sqrt[5]{y}}{r^{4}}}{\log _{3} \frac{\sqrt[4]{x} \cdot \sqrt[5]{y}}{r^{4}}=\square} \square

Studdy Solution
Combine all the expressions obtained from the previous steps:
log3(x4y5r4)=(14log3x+15log3y)4log3r\log_3 \left(\frac{\sqrt[4]{x} \cdot \sqrt[5]{y}}{r^4}\right) = \left(\frac{1}{4} \log_3 x + \frac{1}{5} \log_3 y\right) - 4 \log_3 r
Thus, the expression is:
14log3x+15log3y4log3r\frac{1}{4} \log_3 x + \frac{1}{5} \log_3 y - 4 \log_3 r

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