Question

Can someone please help me get the answer in simple terms?

Answer 1

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`