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

asked Nov 14, 2023 187k views

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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:

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

Lonny answered Nov 20, 2023

by Lonny

8.8k points

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