Question

Solve the system of the equations for $x$ and $y$: $b^{\log x}=a^{\log y}$, where $a>0,b>0$ and $a\ne b,ab\ne 1$

• A. $x=\frac{1}{a}$ and $y=\frac{1}{b}$
• B. $x=\frac{1}{ab}$ and $y=\frac{1}{b}$
• C. $x=\frac{1}{b}$ and $y=\frac{1}{a}$
• D. $x=\frac{1}{a}$ and $y=\frac{1}{ab}$

Answer 1

The correct option is A $x=\frac{1}{a}$ and $y=\frac{1}{b}$

$b^{\log x}=a^{\log y}$
Take logarithm on both the side,
$\log x\log b=\log y\log a$
Clearly, only option 'A' is satisfying this equation. Hence, it is correct choice.