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If 9x=27^y, which of the following expresses x in terms of y [#permalink]
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If \(9x = 27^y\), which of the following expresses x in terms of y? A. \(3^y\) B. \(3^{(y1)}\) C. \(3^{(2y1)}\) D. \(3^{(2y3)}\) E. \(3^{(3y2)}\)
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Originally posted by TheBigCheese on 05 Jul 2008, 11:21.
Last edited by Bunuel on 08 May 2017, 10:09, edited 3 times in total.
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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink]
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05 Jul 2008, 11:27
9x = 27^y => 3^2*x = 3^3y => dividing both sides by 3^2 => x = 3^3y2 Hence E
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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink]
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05 Jul 2008, 14:03
TheBigCheese wrote: If 9x = 27^y, which of the following expresses x in terms of y?
a) 3^y b) 3^y1 c) 3^2y1 d) 3^2y3 e) 3^3y2 9x = 27^y x = (3^3)^y/3^2 x = 3^(3y2)
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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink]
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06 Jul 2008, 18:22
TheBigCheese wrote: If 9x = 27^y, which of the following expresses x in terms of y?
a) 3^y b) 3^y1 c) 3^2y1 d) 3^2y3 e) 3^3y2 9x = 27^y x = 27^y/9 = 3^3y/3^2 = 3^(3y2) E



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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink]
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22 Jan 2012, 07:37



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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink]
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22 Jan 2012, 07:57



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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink]
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23 Jan 2012, 02:15
Baten80 wrote: What's wrong if i solve the problem as follows: 3*3x=3*9^y 3x = 9^y [Dividing both side by 3] x = 3^(2y1) Ans. C. Please help to correct my wrong concept as the OA is E. Bunuel has already pointed out your error so I will not repeat it. Let me give you another method of working out the solution here (though you should ensure that you understand the theory of exponents well) If 9x = 27^y, which of the following expresses x in terms of y? A. 3^y B. 3^(y1) C. 3^(2y1) D. 3^(2y3) E. 3^(3y2) We need x in terms of y. In 9x = (27)^y, put y = 0. You get x = 1/9 Now see which option will give you 1/9 when you put y = 0. I hope you can quickly see that only option (E) will give you x = 1/9 when y = 0. Answer is (E). Such methods work well when you have variables in the options. Note: If more than one options had given 1/9, you could have tried some other values to choose the right answer out of those options.
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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink]
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23 Jan 2012, 08:06
9x=27^y 3^2x=3^3y devide both sides by 3^2 x=3^3y2. note, you need to make both sides have equale exponent, and remember when you simplify exponents through division, you subtract them
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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink]
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08 Apr 2012, 22:41
To Karishma,
I'm glad you used the same approach as I've used, but I used y=1, which makes, 9x = 27^y 9x = 27 x = 3. Look for options which give ans. as x=3, I marked A (option E also gives x=3), which gives x=3 which is wrong ans. Can u explain where I'm wrong
Thnx, Priyal



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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink]
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09 Apr 2012, 05:28
priyalr wrote: To Karishma,
I'm glad you used the same approach as I've used, but I used y=1, which makes, 9x = 27^y 9x = 27 x = 3. Look for options which give ans. as x=3, I marked A (option E also gives x=3), which gives x=3 which is wrong ans. Can u explain where I'm wrong
Thnx, Priyal When you put y = 1, three of the five options give you x = 3 (options A, C and E). Any one of these 3 could be the correct answer. You now need to try out some other values of y to get the answer out of these 3 options. You need to check all the options to ensure that no other options gives you the same value. When I put y = 0, I try it in all the options and only option E gives me 1/9 so I can directly mark that as the answer. This is the reason I mentioned the note in the post above: "Note: If more than one options had given 1/9, you could have tried some other values to choose the right answer out of those options." So now your next step is to put y = 0 and out of the 3 options, only E will satisfy x = 1/9. Try and put the easiest value first. Easiest value is generally 0, if allowed. Putting y = 2/3/4... will make it cumbersome.
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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink]
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25 Jun 2013, 05:55



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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink]
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25 Jun 2013, 08:51
Bunuel wrote: Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE9x=27^y 3^2 x = 3^3y Clearly, x=1 an y=2/3 will satisfy Now we have the values of x given in the options, substitute y=2/3 , wherever we get value =1, is the answer which is clearly E since only that has 3 multiplied with y which conveniently cancels our denominator and results in 3^0 =1 Ans=>E
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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink]
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26 Feb 2014, 23:26
27 can be written as 9^ 3/2 So x = 9^(3y/21) x = 3^(3y2) = Answer = E
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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink]
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08 May 2017, 23:49
\((3)^{2}\)x= \((3)^{3y}\) So x= \((3)^{3y}\)/\((3)^{2}\) x= \((3)^{3y2}\) Answer: E. Kudos please if you like my explanation!
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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink]
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12 May 2017, 13:33
TheBigCheese wrote: If \(9x = 27^y\), which of the following expresses x in terms of y?
A. \(3^y\)
B. \(3^{(y1)}\)
C. \(3^{(2y1)}\)
D. \(3^{(2y3)}\)
E. \(3^{(3y2)}\) Let’s simplify the given equation: 9x = 27^y (3^2)x = 3^(3y) x = 3^(3y)/3^2 x = 3^(3y2) Answer: E
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