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

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

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New post 21 Jul 2016, 23:07
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

80% (01:34) correct 20% (01:41) wrong based on 91 sessions

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Kudos [?]: 135428 [0], given: 12694

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Joined: 26 Nov 2012
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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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New post 22 Jul 2016, 00:57
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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New post 22 Jul 2016, 01:36
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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New post 22 Jul 2016, 01:51
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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New post 11 Sep 2017, 06:41
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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, 06:41
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