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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
Joined: 20 Jan 2013
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Location: India
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, 20:12
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83% (01:17) correct 17% (08:00) wrong based on 208 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
[Reveal] Spoiler: OA
Intern
Joined: 21 Jul 2013
Posts: 14
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, 21:21
1
KUDOS
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
Joined: 12 May 2013
Posts: 79
Re: If 4^(2X + 1) + 4^(X+1) = 80. Find value of X [#permalink]

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07 Nov 2014, 01:31
3
KUDOS
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
Posts: 129
Re: If 4^(2X + 1) + 4^(X+1) = 80. Find value of X [#permalink]

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07 Nov 2014, 03:54
3
KUDOS
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: 14
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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09 Nov 2014, 21:01
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

Last edited by SergeRobu on 11 Nov 2014, 01:43, edited 1 time in total.
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Re: If 4^(2X + 1) + 4^(X+1) = 80. Find value of X [#permalink]

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11 Nov 2014, 01:22
11
KUDOS
1
This post was
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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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Joined: 09 Sep 2013
Posts: 13742
Re: If 4^(2X + 1) + 4^(X+1) = 80. Find value of X [#permalink]

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16 Jan 2016, 10:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If 4^(2X + 1) + 4^(X+1) = 80. Find value of X [#permalink]

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08 Mar 2016, 07:05
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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Re: If 4^(2X + 1) + 4^(X+1) = 80. Find value of X [#permalink]

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18 May 2017, 20:54
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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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, 18:32
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   [#permalink] 27 Sep 2017, 18:32
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