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Exponents .. logic.. please explain !

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Exponents .. logic.. please explain ! [#permalink] New post 25 Jul 2012, 07:24
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Hai all

I am just not getting this logic.. just help me with this


(x+4)^1/2^2 = 3

Now if we simplify this is : x+4 = 3 so I get x=-1

However I can see in the solution that [ x+4 ]= 3 (i.e modulus)

so x=-1 or -7

Please explain !
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Magoosh GMAT Instructor
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Re: Expoents .. logic.. please explain ! [#permalink] New post 25 Jul 2012, 07:36
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Priyanka2011 wrote:
Hai all

I am just not getting this logic.. just help me with this

(x+4)^1/2^2 = 3

Now if we simplify this is : x+4 = 3 so I get x=-1. However I can see in the solution that [ x+4 ]= 3 (i.e modulus) so x=-1 or -7

Please explain!


I would love to help you with this, but first of all, I need to know what is the source of this question? And more importantly, I need it to be written in proper mathematical syntax. What you have is sloppy and unclear. What you have written I interpret as . . .

[(x+4)^1/2]^2 = 3

but that has a solution of only x = -1. The problem

[(x+4)^2]^(1/2) = 3

would have a solution of both x = -1 and x = -7, but that doesn't appear consistent with what you have written.

If you clarify the problem, with proper mathematical syntax, I will be better able to help you. Here are a couple blog articles that might help you.
http://magoosh.com/gmat/2012/exponent-p ... -the-gmat/
http://magoosh.com/gmat/2012/exponent-p ... -the-gmat/

Mike :-)

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Mike McGarry
Magoosh Test Prep

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Re: Expoents .. logic.. please explain ! [#permalink] New post 25 Jul 2012, 07:46
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Hai.. sorry for the bad usage of syntax.. yeah what you have inferred is absolutely right !

[(x+4)^2]^(1/2) = 3

If the problem is as above, how is x=-7 ( i get the other part being simple ! )
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Magoosh GMAT Instructor
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Re: Expoents .. logic.. please explain ! [#permalink] New post 25 Jul 2012, 08:29
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Priyanka2011 wrote:
Hai.. sorry for the bad usage of syntax.. yeah what you have inferred is absolutely right !

[(x+4)^2]^(1/2) = 3

If the problem is as above, how is x=-7 ( i get the other part being simple ! )


Well, there are a few ways to approach this ---- the straightforward algebraic way would be to solve for x -----

[(x+4)^2]^(1/2) = 3
undo the power of 1/2 by squaring both sides
(x+4)^2 = 9
take a square root of both sides, remembering the +/- sign
x+4 = +/-3, which means x = -1 and x = -7

The equation u^2 = 9 must have two solutions, u = +3 and U = -3, because (3)^9 and also (-3)^2 = 9

Another way to go about it is to plug in the solution x = -7 to verify that it satisfies the equation.
[(x+4)^2]^(1/2) = [(-7+4)^2]^(1/2) = [(-3)^2]^(1/2) = 9^(1/2) = 3
so, x = -7 checks out --- it is a valid solution for this equation.

Notice, even though u^2 = 9 has two solutions, the positive root and the negative root, the expression 9^(1/2) has only one output, just the positive root.

Does all this make sense? Please let me know if you have any further question.

Mike :-)

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Mike McGarry
Magoosh Test Prep

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Re: Expoents .. logic.. please explain !   [#permalink] 25 Jul 2012, 08:29
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