1 Answer

GertV · Answer 1 · 2023-03-22T10:59:58+0000

Solution:

Given the expression:

$\log _(10)xy^2$

From the multiplication law of logarithm,

$\log _cAB=\log _cA+\log _cB$

thus, we have

$\log _(10)xy^2=\log _(10)x+\log _(10)y^2$

From the power law of logarithm,

$\begin{gathered} \log _cA^b=b*\log _cA \\ =b\log _cA \end{gathered}$

this then implies that

$\begin{gathered} \log _(10)xy^2=\log _(10)x+\log _(10)y^2 \\ =\log _(10)x+(2*\log _(10)y) \\ =\log _(10)x+2\log _(10)y \\ \end{gathered}$

Hence, when the above expression is expanded, we have

$\log _(10)x+2\log _(10)y$

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