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

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Intern
Joined: 10 Jun 2008
Posts: 8

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

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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

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

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Joined: 30 Apr 2008
Posts: 1870

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

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

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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 $$3^{3a+4}=9^a$$

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$$. GMAT Club Premium Membership - big benefits and savings Kudos [?]: 607 [0], given: 32 SVP Joined: 30 Apr 2008 Posts: 1870 Kudos [?]: 607 [0], given: 32 Location: Oklahoma City Schools: Hard Knocks Re: I think I used the right method but not sure why I am wrong! [#permalink] Show Tags 16 Aug 2008, 14:34 The way you did it is correct. if a = -4, the 3(-4)+4 = -8, so we have $$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}$$ darlameow wrote: Question, What is the value of (a) if 3^3a+4=9^a 3^3a+4=3^2a 3a+4=2a a=-4 but the answer key says the answer should be 4 Any suggestions! Thanks........ _________________ ------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

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

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

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

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