Question

Solve for the value of $x$ in $(25{)}^{x-2}=(125{)}^{2x-4}$

• A. $\frac{3}{4}$
• B. $0$
• C. $2$
• D. $-2$

Answer 1

Answer: (C)

$2$

The given equation is

${\left(25\right)}^{x-2}={\left(125\right)}^{2x-4}\Rightarrow {\left(5^2\right)}^{x-2}={\left(5^3\right)}^{2x-4}\Rightarrow 5^{2(x-2)}=5^{3(2x-4)}\Rightarrow 2(x-2)=3(2x-4)\Rightarrow 6x-2x=12-4\Rightarrow x=2$