Aggh, I'm so fuzzy on this. This is a problem from the CLEP practice test. I'm putting parenthesis around things that are exponents, since there's no way to denote them:


If 8(x) = 15 and 8(y) = 25, then 8(2x +y) = ??????

I can't for the life of me remember how to work this problem and digging through my old math books shed no light. Any ideas?

Did you mean
8^x = 15
8^y = 25
8^(2x+y) = ??

I couldn't figure it out either, but I posted this on another forum and they said,

"since 8x = 15 ... 82x = (8x)2 = 152.

82x+y = 82x*8y = 152*25"

Hope this helps!

I think (x =15 and (y)=25, therefore 8 x (2 x 15+ 25)
(30 +25) = 55
8 x 55 = 440

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MCSE (2003k), CCNP, Project+

I believe this is how it works. There's a rule involving multiplying exponents with the same base number, so:
8^(2x + y) is the same as
8^(2x) + 8^(y) which is the same as
8^x + 8^x + 8^y
= 15 + 15 + 25
= 55

If you would provide the correct answer, that would help with reverse engineering the rule/method, because I might be remembering the rule incorrectly.

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Steve, Webmaster

Ok...There are two ways to solve this problem...One is the use of Logs to find an unknown exponent. For example:
8^x=15
= log 15 base 8 = x (re-write in log form)
=log 15 / log 8 (divide)
=1.3022968652 (this is the "x" exponent)

8^y=25
=log 25 base 8 = y
=log 25 / log 8
= 1.54795206326 (this is the "y" exponent)

Plug your now Known exponents into your equation:
8^2x+y = 8^2(1.3022968652)+(1.54795206326) = 5624.9999 = 5625

Second Way:
They made this easy because of the same base 8.
8^x=15 , 8^y=25, 8^2x+y=??
8^2x+y = 8^2x * 8^y (re-write by seperating exponents)
8^y is the easy part, we know that is 25
8^2x is not the same of course as 8^x (which we know is 15) so what makes it different? Yes the "2". Well you squared the left side of the equation so you have to square the right side: 8^2x = 15^2. Now you know 8^2x = 225 (15 squared).
So put the two together: 8^2x * 8^y is now the same as 225*25 = 5625

^ = raised to that exponent
* = multiplication

I hope this helps. It is a tough problem to explain on a message board.
Best regards,
Jason

You have the problem set up nicely, however, you should multiply in rows 2, 3, and 4 instead of add. You can "split" the exponent, but you then must multiply. For example: If you had x^2+3; that would equal (x^2)(x^3), the bases are the same and in multiplication you would simply add the exponents making it x^5.
You could not put them back together if you split them like this: x^2 + x^3. They would not be "like" terms, one is squared and the other cubed.

I hope this helps with your reverse engineering because I am not familiar with that method.

Best Regards,
Jason

For this particular problem, you will square 15 which will give you 225 then mulitiply 225 by 25 which will give you 5625. I had a hard time figuring this one out when I was studying for the college math clep. I just played with it until I got the correct answer.

Yeah, that looks right. Thanks Jason--I couldn't remember exactly how the rule went.

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Steve, Webmaster