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

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

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New post 06 Nov 2014, 21:12
3
00:00
A
B
C
D
E

Difficulty:

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

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New post 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

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

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

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

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

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New post Updated on: 11 Nov 2014, 02:43
adymehta29 wrote:
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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Re: If 4^(2X + 1) + 4^(X+1) = 80. Find value of X  [#permalink]

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

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