ABC26GN2043 · Logarithms

Subject: General Aptitude · Chapter: Logarithms · Exam: · Marks: · Difficulty:

If $a^{x}=b^{y}$, 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

Answer

Answer (as printed): C

Explanation

$$\begin{aligned} a^{x}=b^{y} \Rightarrow \log a^{x} & =\log b^{y} \\ \Rightarrow x \log a & =y \log b \Rightarrow \frac{\log a}{\log b}=\frac{y}{x} . \end{aligned}$$

Explanation as extracted from the printed page; notation may be imperfect.

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