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Write each expression as a sum or difference or multiple of logarithms, assume the variables represents positive numbers

Write each expression as a sum or difference or multiple of logarithms, assume the-example-1
User Moussa
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6 votes

SOLUTION

The given expression is:


\log_6(4x)/(3)

This is simplified to give


\operatorname{\log}_6(4x)/(3)=\operatorname{\log}_64x-\operatorname{\log}_63

This further gives


\operatorname{\log}_64x-\operatorname{\log}_63=\operatorname{\log}_64+\operatorname{\log}_6x-\operatorname{\log}_63

Therefore the required answer is:


\begin{equation*} \operatorname{\log}_64+\operatorname{\log}_6x-\operatorname{\log}_63 \end{equation*}

User Lonny
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