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# If 4^(2X + 1) + 4^(X+1) = 80. Find value of X

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Manager
Status: I am not a product of my circumstances. I am a product of my decisions
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Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
If 4^(2X + 1) + 4^(X+1) = 80. Find value of X  [#permalink]

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06 Nov 2014, 21:12
3
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25% (medium)

Question Stats:

83% (01:16) correct 17% (07:51) wrong based on 218 sessions

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If 4^(2X + 1) + 4^(X+1) = 80. Find value of X

A) -5
B) 0
C) 1
D) 4
E) 5
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1834
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If 4^(2X + 1) + 4^(X+1) = 80. Find value of X  [#permalink]

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11 Nov 2014, 02:22
11
1
Ashishmathew01081987 wrote:
If 4^(2X + 1) + 4^(X+1) = 80. Find value of X

A) -5
B) 0
C) 1
D) 4
E) 5

$$4^{(2X + 1)} + 4^{(X+1)} = 80$$

$$4^{2X} * 4 + 4^X * 4 = 80$$

$$4^{2X} + 4^X = 20$$

$$4^{2X} + 4^X = 4 * 5$$

$$4^X (4^X + 1) = 4^1 (4^1 + 1)$$

Both LHS & RHS are similar; X = 1

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##### General Discussion
Intern
Joined: 21 Jul 2013
Posts: 13
Location: Moldova, Republic of
GMAT 1: 610 Q47 V28
GPA: 3.62
Re: If 4^(2X + 1) + 4^(X+1) = 80. Find value of X  [#permalink]

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06 Nov 2014, 22:21
1
If 4^(2X + 1) + 4^(X+1) = 80. Find value of X :

We can rewrite the equation: 4*(4^(2x)+4^(x))=4^(2)*5 => 4^(2x)+4^(x)=4*5.
Let 4^(x)=y, and we have y^(2)+y=20 or (y-4)(y+5)=0 therefor y=4 or y=-5.
Let take y=4, and we have 4^(x)=4^(1) => x=1. The answer is C.
Manager
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Re: If 4^(2X + 1) + 4^(X+1) = 80. Find value of X  [#permalink]

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07 Nov 2014, 02:31
3
The easy way of solving this sums is to substitute the value of X with the answer choices and we will get the answer B.
Manager
Joined: 20 Dec 2013
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Re: If 4^(2X + 1) + 4^(X+1) = 80. Find value of X  [#permalink]

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07 Nov 2014, 04:54
3
Ashishmathew01081987 wrote:
If 4^(2X + 1) + 4^(X+1) = 80. Find value of X

A) -5
B) 0
C) 1
D) 4
E) 5

4^3 + 4^2 = 80 hence the value of x is 1.
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Intern
Joined: 21 Jul 2013
Posts: 13
Location: Moldova, Republic of
GMAT 1: 610 Q47 V28
GPA: 3.62
If 4^(2X + 1) + 4^(X+1) = 80. Find value of X  [#permalink]

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Updated on: 11 Nov 2014, 02:43
The easy way of solving this sums is to substitute the value of X with the answer choices and we will get the answer B.

Agree... in this case the easiest way is to replase x with answers but in case if x were 4 or bigger, it would be harder... One KUDOS for u

Originally posted by SergeRobu on 09 Nov 2014, 22:01.
Last edited by SergeRobu on 11 Nov 2014, 02:43, edited 1 time in total.
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Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If 4^(2X + 1) + 4^(X+1) = 80. Find value of X  [#permalink]

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08 Mar 2016, 08:05
Serje wrote:
If 4^(2X + 1) + 4^(X+1) = 80. Find value of X :

We can rewrite the equation: 4*(4^(2x)+4^(x))=4^(2)*5 => 4^(2x)+4^(x)=4*5.
Let 4^(x)=y, and we have y^(2)+y=20 or (y-4)(y+5)=0 therefor y=4 or y=-5.
Let take y=4, and we have 4^(x)=4^(1) => x=1. The answer is C.

I did it the same way ...But here i this we can use the options to check the sides ....That actually is easy here.
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Intern
Joined: 04 Aug 2017
Posts: 10
Re: If 4^(2X + 1) + 4^(X+1) = 80. Find value of X  [#permalink]

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27 Sep 2017, 19:32
I approached this problem a little differently than the other posters but most of the methodology is still pretty much the same:

4^2x+1 + 4^x+1=80
4^2x+1 + 4^x+1=4^3 + 4^2
2x+1+x+1=3+2
3x+2=5
3x=3
x=1
Re: If 4^(2X + 1) + 4^(X+1) = 80. Find value of X &nbs [#permalink] 27 Sep 2017, 19:32
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# If 4^(2X + 1) + 4^(X+1) = 80. Find value of X

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