Solution:
Given the expression:
[tex]\log _{10}xy^2[/tex]
From the multiplication law of logarithm,
[tex]\log _cAB=\log _cA+\log _cB[/tex]
thus, we have
[tex]\log _{10}xy^2=\log _{10}x+\log _{10}y^2[/tex]
From the power law of logarithm,
[tex]\begin{gathered} \log _cA^b=b\times\log _cA \\ =b\log _cA \end{gathered}[/tex]
this then implies that
[tex]\begin{gathered} \log _{10}xy^2=\log _{10}x+\log _{10}y^2 \\ =\log _{10}x+(2\times\log _{10}y) \\ =\log _{10}x+2\log _{10}y \\ \end{gathered}[/tex]
Hence, when the above expression is expanded, we have
[tex]\log _{10}x+2\log _{10}y[/tex]
