Question

Find x, if:

$(\sqrt{\frac{3}{5}}{)}^{x+1}=\frac{125}{27}$

• A. -7
• B. 7
• C. 8
• D. -8

Answer 1

The correct option is A -7

${\left(\sqrt{\frac{3}{5}}\right)}^{x+1}=\frac{125}{27}$
${\left(\frac{3}{5}\right)}^{\frac{x+1}{2}}=\frac{5^3}{3^3}$
${\left(\frac{3}{5}\right)}^{\frac{x+1}{2}}={\left(\frac{3}{5}\right)}^{-3}$
$\Rightarrow \frac{x+1}{2}=-3$
$\Rightarrow x+1=-6\Rightarrow x=-7$