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Question
If ax = by, then:
Options:
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: Option C
$$\eqalign{
& {a^x} = {b^y} \cr
& \Rightarrow \log {a^x} = \log {b^y} \cr
& \Rightarrow x\log a = y\log b \cr
& \Rightarrow {{\log a} \over {\log b}} = {y \over x} \cr} $$

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