Question

Find the value of x, if $(\frac{5^x}{5^3}{)}^2=5^{15}$.

• A. $\frac{25}{2}$
• B. $\frac{23}{2}$
• C. $\frac{21}{2}$
• D. $\frac{21}{3}$

Answer 1

The correct option is C $\frac{21}{2}$

Given, $(\frac{5^x}{5^3}{)}^2=5^{15}$
By the Laws of Exponents, we know that
$(a^m{)}^n=a^{mn}$
$⟹(\frac{5^x}{5^3}{)}^2=\frac{5^{2x}}{5^6}$

$⟹\frac{5^{2x}}{5^6}=5^{15}$
Using laws of exponents,
$\frac{a^m}{a^n}=a^{m-n}$
$⟹\frac{5^{2x}}{5^6}=5^{2x-6}=5^{15}$
Since, the bases are same so equating the powers, we get
$2x-6=15⟹2x=15+6=21⟹x=\frac{21}{2}$