Exponent addition question.

[pistolpete]

Hello,
I am trying to figure out this problem:

If 5^n + 5^n + 5^n + 5^n + 5^n = 5^25 then what is the integer n that satisfies this equation?

I know that when adding exponents, I do not add the exponents together. Instead I add the base with its exponent to the other bases with their exponents. I know that 5^25 = 2.980232239 x 10^17. I am trying different integers and plugging them in for n and then addint all five of them to see if I can get that exact large number...but I can't get it...any help?

EDIT: I got it! n = 24.

[stapel_eliz]

If 5^n + 5^n + 5^n + 5^n + 5^n = 5^25 then what is the integer n that satisfies this equation?

You have five copies of 5ⁿ, which (converting the addition to multiplication) means you have:

. . . . .5 * 5ⁿ = 5¹ * 5ⁿ = 5^{1 + n} = 5²⁵

Then 1 + n = 25.

EDIT: I got it! n = 24.

Excellent!