Expand each logarithm as much as possible to rewrite each expression as a sum, difference or product of logs.

asked Mar 22, 2023 99.1k views

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In order to expand this logarithm, we can use the following property:

$\log_a(b\cdot c)=\log_ab+\log_ac$

So, expanding the given logarithm, we have:

$\begin{gathered} \log_b(7x\cdot2y)\\ \\ =\log_b7x+\log_b2y\\ \\ =\log_b7+\log_bx+\operatorname{\log}_b2+\operatorname{\log}_by \end{gathered}$

Lockyer answered Mar 26, 2023

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