Question

If $(\frac{a}{b}{)}^{x-1}=(\frac{b}{a}{)}^{x-3}$, then the value of $x$ is:

• A. $\frac{1}{2}$
• B. 1
• C. 2
• D. $\frac{7}{2}$

Answer 1

The correct option is C 2

Given $(\frac{a}{b}{)}^{x-1}=(\frac{b}{a}{)}^{x-3}$
$\Rightarrow (\frac{a}{b}{)}^{x-1}=(\frac{a}{b}{)}^{-(x-3)}=(\frac{a}{b}{)}^{(3-x)}$
$\Rightarrow x-1=3-x$
$\Rightarrow 2x=4$
$\Rightarrow x=2$