Question

If $a^{3-x}{b}^{5x}=a^{x+5}{b}^{3x}$, then the value of $x\log \left(\frac{b}{a}\right)$ is:

• A. $\log a$
• B. $\log b$
• C. $\log x$
• D. $1$

Answer 1

The correct option is A $\log a$

$a^{3-x}{b}^{5x}=a^{x+5}{b}^{3x}$ [use $\log x-\log y=\log \left(\frac{x}{y}\right)$]

$\Rightarrow a^{x+5+x-3}{b}^{3x-5x}=1$

$\Rightarrow b^{2x}=a^{2x+2}=a^{2x}{a}^2$ (take log)

$\Rightarrow 2x\log b=2x\log a+2\log a\Rightarrow x\log \left(b/a\right)=\log a$