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# Quant Exp Q in Subt equation

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Intern
Joined: 09 Jan 2009
Posts: 10
Schools: harvard
Quant Exp Q in Subt equation [#permalink]

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28 Jan 2009, 10:54
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Question: (3^x)-3^(x-1)=162 what does x(x-1)= the answer is 20? what is the rule for manipulating exponents with like bases but subtration?

Answer: you need to factor it out: so
3^(x-1)*3-3^(x-1)=3^(x-1)(3-1)=162. Then find x.

Follow up: What exactly did you factor out? It looks like you changed the original equation? Can you follow up with more specific explanation?
Senior Manager
Joined: 30 Nov 2008
Posts: 482
Schools: Fuqua
Re: Quant Exp Q in Subt equation [#permalink]

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28 Jan 2009, 12:26
From eq it is given, 3 power x - 3 power (x-1) = 162.

==> taking 3 power (x-1) common on the LHS, it will translated to (3 power (x-1))(3 - 1) = 162.

==> 3 power (x-1) * 2 = 162
==> 3 power (x-1) = 81
==> 3 power (x-1) = 3 power 4(81 can be expressed as 3 power 4)
==> bases are equal which is 3, hence powers should be equal.
==> x-1 = 4 ==> x = 5.

Now coming back to the question, what is x(x-1)?

since x = 5, x(x-1) = 5*4 = 20 is the Ans.

Hope you got it.
Intern
Joined: 09 Jan 2009
Posts: 10
Schools: harvard
Re: Quant Exp Q in Subt equation [#permalink]

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29 Jan 2009, 11:38
In analyzing the first step (where you factor out 3 power x-1), and are left with (3-1).
If you take out a 3^x-1 how are you left with only (3-1)? I would think if you multiplied it back through you would get 9^x-1 - 3^x-1 and not the original equation.
Re: Quant Exp Q in Subt equation   [#permalink] 29 Jan 2009, 11:38
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# Quant Exp Q in Subt equation

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