Question

Find the value of $x$ if
$\left(\frac{625}{81}\right)\times (\frac{125}{27}{)}^x=(\frac{25}{9}{)}^8$

• A. 4
• B. 5
• C. -3
• D. -4

Answer 1

The correct option is A 4

$\left(\frac{625}{81}\right)\times (\frac{125}{27}{)}^x=(\frac{25}{9}{)}^8$
$\left(\frac{5^4}{3^4}\right)\times (\frac{5^3}{3^3}{)}^x=(\frac{5^2}{3^2}{)}^8$
$(\frac{5}{3}{)}^4\times ((\frac{5}{3}{)}^3{)}^x=((\frac{5}{3}{)}^2{)}^8$
$(\because \frac{a^m}{b^m}=(\frac{a}{b}{)}^m)$
$(\frac{5}{3}{)}^4\times (\frac{5}{3}{)}^{3x}=(\frac{5}{3}{)}^{16}$
$(\because (a^m{)}^n=a^{m\times n})$
$(\frac{5}{3}{)}^{4+3x}=(\frac{5}{3}{)}^{16}$
$(\because a^m\times a^n=a^{m+n})$
$\Rightarrow 4+3x=16$
$\Rightarrow 3x=16-4=12$
$x=\frac{12}{3}=4$
Hence, the value of $x$ is 4.