Question

25^x+1 - 5^x+1 = 100​

Answer 1

Do you mean 25^(x+1) - 5^(x+1) = 100 ?

25^(x+1) - 5^(x+1) = 100
(5^2)^(x+1) - 5^(x+1) = 100
5^(2(x+1)) - 5^(x+1) = 100
5^(2(x+1)) - 5^(x+1) - 100 = 0

Quadratic Formula
5^(x+1) = [1 ± ⎷(1^2-4(1)(-100))]/[2(1)]
5^(x+1) = [1 ± ⎷401]/2

x+1 = log₅([1 + ⎷401]/2)= log₅(1 + ⎷401) - log₅(2)
x = log₅(1 + ⎷401) - log₅(2) - 1

Answer 2

we need to bring together the terms containing x. Then constant terms on the other side. Then simplify by performing the addition/subtraction/multiplication.

Done hope it helps