Question

If ${\left(\frac{7}{5}\right)}^3\times {\left(\frac{7}{5}\right)}^{x+2}={\left(\frac{7}{5}\right)}^8$, then $x=$.

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

The correct option is A $3$

Given, ${\left(\frac{7}{5}\right)}^3\times {\left(\frac{7}{5}\right)}^{x+2}={\left(\frac{7}{5}\right)}^8$

Given equation can be written as,

${\left(\frac{7}{5}\right)}^{3+x+2}={\left(\frac{7}{5}\right)}^8$

Comparing the powers, we get

$x+5=8$

$\Rightarrow x=3$