5^x-1<25

To solve this inequality, we need to isolate the variable x.

First, we can simplify the left side by using the exponent rule that says a^m / a^n = a^(m-n).

So, we have:

5^(x-1) < 25

Next, we can write 25 as 5^2, since 5^2 = 25.

So, we have:

5^(x-1) < 5^2

Now we can use the property that if a^x < a^y, then x < y.

So, we can conclude:

x-1 < 2

Adding 1 to both sides, we get:

x < 3

Therefore, the solution to the inequality is:

x < 3.