Question
If $${\log _{10}}a = p,$$ $${\log _{10}}b = q,$$ then what is $${\log _{10}}\left( {{a^p}{b^q}} \right)$$ equal to?
Answer: Option A
$$\eqalign{
& {\text{Given}}, \cr
& {\log _{10}}a = p,\,{\log _{10}}b = q \cr
& {\log _{10}}\left( {{a^p}{b^q}} \right) = {\log _{10}}{a^p} + {\log _{10}}{b^q} \cr
& = p{\log _{10}}a + q{\log _{10}}b \cr
& = {p^2} + {q^2} \cr} $$
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$$\eqalign{
& {\text{Given}}, \cr
& {\log _{10}}a = p,\,{\log _{10}}b = q \cr
& {\log _{10}}\left( {{a^p}{b^q}} \right) = {\log _{10}}{a^p} + {\log _{10}}{b^q} \cr
& = p{\log _{10}}a + q{\log _{10}}b \cr
& = {p^2} + {q^2} \cr} $$
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