Question

0. 7. If 25^x-1 = 5^2x-1-100, then find x.​

Answer 1

As it is clearly seen, the entire problem statement is asking for a simplification using exponent rules, looking at the expression 25x– 1 = 52x– 1 – 100, it is observed that 25x – 1 can be written as (52)x – 1,

(52)x – 1 = 52x – 1 – 100

Power Rule ⇢ (an)m = an × m

5(2x – 2) = 5(2x – 1) – 100

5(2x-1) – 5(2x-2) = 100

5(2x – 2) (5 – 1) = 100

5(2x – 2) = 25

5(2x – 2) = 52

2x – 2 = 2

2x = 4

x = 2