ABC26GN2101 · Logarithms
Subject: General Aptitude · Chapter: Logarithms · Exam: 2012 · Marks: · Difficulty:
If $\log_{10}a=p$ and $\log_{10}b=q$, then what is $\log_{10}\left(a^{p}b^{q}\right)$ equal to ? (CDS, 2012)
(a)$p^{2}+q^{2}$
(b)$p^{2}-q^{2}$
(c)$p^{2}q^{2}$
(d)$\frac{p^{2}}{q^{2}}$
Answer
Explanation
Given $\log_{10}a=p, \log_{10}b=q$. $\log_{10}\left(a^{p}b^{q}\right)=\log_{10}a^{p}+\log_{10}b^{q}=p\log_{10}a+q\log_{10}b=p^{2}+q^{2}$
Explanation as extracted from the printed page; notation may be imperfect.
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