solve for x without using a calculator

Question

5^(x+1) = 25

i know that x would equal 1 because 5^2 is 25, but i don't know how to show how to solve it

All you need to do is what you just did: Explain that if x = 1, the equation is satisfied.

If you are looking for a method of solution other than a guess that happens to work, take the log of both sides of the equation.
(x+1) log 5 = log 25
x+1 = log 25/log 5 = (log 5^2)/log5
= (2 log 5)/log 5 = 2
x = 1

solve for x without using a calculator
5^(x+1) = 25

5^(x + 1) = 25 = 5^2

Therefore, (x + 1) = 2 making x = 1.

Answer 1

(x+1)(x-1)=5(x-1)