Question

If ${\left(\frac{a}{b}\right)}^{x-1}={\left(\frac{b}{a}\right)}^{x-3}$, then find $x$.

• A. $2$
• B. $1$
• C. $3$
• D. $4$

Answer 1

The correct option is A $2$

${\left(\frac{a}{b}\right)}^{x-1}={\left(\frac{b}{a}\right)}^{x-3}$

$\Rightarrow {\left(\frac{a}{b}\right)}^{x-1}={\left(\frac{a}{b}\right)}^{-(x-3)}$

$\Rightarrow {\left(\frac{a}{b}\right)}^{x-1}={\left(\frac{a}{b}\right)}^{3-x}$

$\Rightarrow x-1=3-x$

$\Rightarrow 2x=4$

$\Rightarrow x=2$