Question

Find x, if:

$(3\sqrt{\frac{2}{3}}{)}^{x-1}=\frac{27}{8}$

• A. 8
• B. -8
• C. 7
• D. -7

Answer 1

The correct option is B -8

$\Rightarrow {\left(3\sqrt{\frac{2}{3}}\right)}^{x-1}=\frac{27}{8}$
$\Rightarrow {\left(\frac{2}{3}\right)}^{\frac{x-1}{3}}=\frac{3^3}{2^3}$
$\Rightarrow {\left(\frac{2}{3}\right)}^{\frac{x-1}{3}}={\left(\frac{2}{3}\right)}^{-3}$
$\Rightarrow \frac{x-1}{3}=-3$
$\Rightarrow x-1=-9$
$\Rightarrow x=-8$