Question

What is the value of $x$, if ${\left(\frac{17}{18}\right)}^{x-1}={\left(\frac{18}{17}\right)}^{x-3}$?

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

Answer 1

The correct option is D $2$

${\left(\frac{17}{18}\right)}^{x-1}={\left(\frac{18}{17}\right)}^{x-3}$

${\left(\frac{17}{18}\right)}^{x-1}={\left(\frac{17}{18}\right)}^{3-x}$

$\therefore x-1=3-x$

$\therefore 2x=4$

$\therefore x=2$