Question

If 25^n-1 + 100 = 5^2n-1, find the value of n.

Answer 1

Answer: n = 2

Explanation:

25^(n-1) + 100 = 5^(2n-1)

25 = 5^2

100 = 4* 5^2

25^(n-1) + 100 = 5^(2n-1)

5^(2n - 2) + 4* 5^2 = 5^(2n-1)

5^(2n - 2) - 5^(2n -1) = -4*5^2

[5^(2n - 1) ]/5 - 5^(2n - 1) = -4*5^2

[5^(2n-1)] ( 1/5 - 1) = -4*5^2

(-4/5) * [5^(2n-1)] = -4*5^2

5^(2n-1) = 5^3

2n - 1 = 3

2n = 4

n = 2

From MysticAlanCheng