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1. 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

Solution:

\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}

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