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I think I used the right method but not sure why I am wrong!

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Joined: 10 Jun 2008
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I think I used the right method but not sure why I am wrong! [#permalink]

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New post 14 Aug 2008, 17:47
Question, What is the value of (a) if 3^3a+4=9^a
3^3a+4=3^2a
3a+4=2a
a=-4
but the answer key says the answer should be 4

Any suggestions! Thanks........

Kudos [?]: 1 [0], given: 0

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Joined: 30 Apr 2008
Posts: 1870

Kudos [?]: 607 [0], given: 32

Location: Oklahoma City
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Re: I think I used the right method but not sure why I am wrong! [#permalink]

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New post 14 Aug 2008, 17:49
Is the formatting I applied correct? Is this a DS question? If so, please label the statements. If it's a PS, then I guess the part below the question is your work from when you answered it?
darlameow wrote:
Question, What is the value of (a) if \(3^{3a+4}=9^a\)

but the answer key says the answer should be 4

Any suggestions! Thanks........

_________________

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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 607 [0], given: 32

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Joined: 30 Apr 2008
Posts: 1870

Kudos [?]: 607 [0], given: 32

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Re: I think I used the right method but not sure why I am wrong! [#permalink]

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New post 16 Aug 2008, 14:34
The way you did it is correct. if a = -4, the 3(-4)+4 = -8, so we have \(3^{-8}\) and \(9^{-4}\) These both are equal to:

\(\frac{1}{3^8}\) and \(\frac{1}{9^4}\); \(9^4 = (3^2)^4 = 3^8\)

SIDE NOTE:

When dealing with exponents, if you change the base, you obviously have to change the power as well. If you go from \(9^4\) you represent that first as \((3^2)^4\) and then multiply the exponents. So you have \(3^8\) What if you wanted to turn \(3^8\) into a base of 27? \(3^8 = 27^x\), what is x? Take whatever power you used to change the base, such as here, 3 to 27 is a 3 to a power of 3, or \(3^3\), then the existing exponent is divided by the power used to alter the base.

\(3^8 = 27^x\)

\((3^z)^{\frac{8}{z}} = (3^z)^x\) so x = \(\frac{8}{z}\)

In this situation: \(3^8 = 27^x\) x = \(\frac{8}{3}\)



to solve this, we would really need to turn 4 into a power of 3. This power is going to be some fraction such as \(\frac{x}{z}\)

\(\sqrt[z]{3^x}\)

and then to get rid of the root, we'd have to take each other element by a power of z and it would create a horrible mess. I think your answer has to be right at -4 and the OA is wrong. What is the source of this question?

The only way I think it could be different is if the question actually meant \(3^{3a}+4=3^{2a}\)

darlameow wrote:
Question, What is the value of (a) if 3^3a+4=9^a
3^3a+4=3^2a
3a+4=2a
a=-4
but the answer key says the answer should be 4

Any suggestions! Thanks........

_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 607 [0], given: 32

Intern
Intern
avatar
Joined: 10 Jun 2008
Posts: 8

Kudos [?]: 1 [0], given: 0

Re: I think I used the right method but not sure why I am wrong! [#permalink]

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New post 18 Aug 2008, 07:51
Thanks I figured I was right and the practice test was wrong.

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Re: I think I used the right method but not sure why I am wrong!   [#permalink] 18 Aug 2008, 07:51
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