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# If 4^a + 4^(a+1) = 4^(a+2) - 176, what is the value of a?

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Math Expert
Joined: 02 Sep 2009
Posts: 44322
If 4^a + 4^(a+1) = 4^(a+2) - 176, what is the value of a? [#permalink]

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22 Jul 2016, 00:07
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Question Stats:

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If $$4^a + 4^{(a+1)} = 4^{(a+2)} - 176$$, what is the value of a?

A. 1
B. 2
C. 3
D. 4
E. 5
[Reveal] Spoiler: OA

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Re: If 4^a + 4^(a+1) = 4^(a+2) - 176, what is the value of a? [#permalink]

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22 Jul 2016, 01:57
Bunuel wrote:
If 4^a + 4^(a+1) = 4^(a+2) - 176, what is the value of a?

A. 1
B. 2
C. 3
D. 4
E. 5

Check directly by substituting the value.

Sub a = 2 from option B and only this satisfies the condition 16 + 64 = 256 -176 => 80 = 80.

IMO option B is correct option.

OA please...will correct if I missed anything...
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Re: If 4^a + 4^(a+1) = 4^(a+2) - 176, what is the value of a? [#permalink]

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22 Jul 2016, 02:36
Well, I worked it out by doing as follows...
4^a+4^a×4=4^a×4^2-176
4^a×(1+4-16)=-176
4^a×(-11)=-11×16
Thus, 4^a=16
So, a=2
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Re: If 4^a + 4^(a+1) = 4^(a+2) - 176, what is the value of a? [#permalink]

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22 Jul 2016, 02:51
4^a+4*4^a=16*4^a-11*4^2
5*4^a=16*4^a-11*4^2
11*4^2=11*4^a
2=a
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Re: If 4^a + 4^(a+1) = 4^(a+2) - 176, what is the value of a? [#permalink]

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11 Sep 2017, 07:41
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Re: If 4^a + 4^(a+1) = 4^(a+2) - 176, what is the value of a?   [#permalink] 11 Sep 2017, 07:41
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