If $${\log _{10}}a = p,$$   $${\log _{10}}b = q,$$   then what is $${\log _{10}}\left( {{a^p}{b^q}} \right)$$   equal to?

A. p2 + q2

B. p2 - q2

C. p2q2

D. $$\frac{{{p^2}}}{{{q^2}}}$$

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & {\text{Given}}, \cr & {\log _{10}}a = p,\,{\log _{10}}b = q \cr & {\log _{10}}\left( {{a^p}{b^q}} \right) = {\log _{10}}{a^p} + {\log _{10}}{b^q} \cr & = p{\log _{10}}a + q{\log _{10}}b \cr & = {p^2} + {q^2} \cr} $$

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Related Questions on Logarithm

If ax = by, then:

A. $$\log \frac{a}{b} = \frac{x}{y}$$

B. $$\frac{{\log a}}{{\log b}} = \frac{x}{y}$$

C. $$\frac{{\log a}}{{\log b}} = \frac{y}{x}$$

D. None of these