Question

Question:- If 25 ^x-1 = 5 ^2x-1 - 100, then the value of x is_____________.

A) 3

B) 2

C) 4

D) 1

Answer 1

Given,

${25}^{x-1}=5^{2x-1}-100$

$\Rightarrow 5^{2x-2}=5^{2x-1}-100$

$\Rightarrow 5^{2x-1}-5^{2x-2}=100$

$\Rightarrow 5^{2x-1}(1-\frac{1}{5})=100$

$\Rightarrow 5^{2x-1}=100\times \frac{5}{4}$

$\Rightarrow 5^{2x-1}=125=5^3$

$\Rightarrow 2x-1=3$

$\Rightarrow 2x=4$

$\Rightarrow x=2$

Hence, the value of

$x=2$