Question

The values of $x$ satisfying the equation $5^{2x}-5^{x+3}+125=5^x$ are :

• A. $0$ and $2$
• B. $-1$ and $3$
• C. $0$ and $-3$
• D. $0$ and $3$

Answer 1

Answer: (D)

$0$ and $3$

Given equation is: $5^{2x}-5^{x+3}+125=5^x$

Let $5^x=t$
Hence, $t^2-5^3.t+125=t$
$\Rightarrow t^2-126t+125=0$
$\Rightarrow t^2-126t-t+125=0$
$\Rightarrow t(t-125)-1(t-125)=0$
$\Rightarrow (t-1)(t-125)=0$
$\Rightarrow t=1$ and $t=125$
Hence, $5^x=1=5^0$ or $5^x=125=5^3$
Therefore, $x=0$ or $x=3$