Fractions, ratios, percentages, exponents, number patterns, word problems without variables, etc.
pistolpete
Posts: 13
Joined: Wed May 20, 2009 1:07 am
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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
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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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.
EDIT: I got it! n = 24.
Excellent!