Exponent addition question.  TOPIC_SOLVED

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Exponent addition question.  TOPIC_SOLVED

Postby pistolpete on Wed Apr 14, 2010 3:23 pm

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! :D n = 24.
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Postby stapel_eliz on Wed Apr 14, 2010 5:09 pm

pistolpete wrote: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 = 51 + n = 525

Then 1 + n = 25.

pistolpete wrote:EDIT: I got it! :D n = 24.

Excellent! :wink:
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