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# If 16^(2x+3) = 8^(x-1), what is the value of x?

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Math Expert
Joined: 02 Sep 2009
Posts: 62287
If 16^(2x+3) = 8^(x-1), what is the value of x?  [#permalink]

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20 Dec 2019, 00:14
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15% (low)

Question Stats:

95% (01:13) correct 5% (00:59) wrong based on 37 sessions

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If $$16^{2x+3} = 8^{x-1}$$, what is the value of x?

A. -3
B. -1
C. 0
D. 1
E. 3

_________________
HEC & IMD School Moderator
Status: Preparing for GMAT
Joined: 16 Dec 2018
Posts: 828
Location: Italy
WE: Engineering (Manufacturing)
Re: If 16^(2x+3) = 8^(x-1), what is the value of x?  [#permalink]

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20 Dec 2019, 00:54
$$16^{2x+3} = 8^{x-1}$$ .... (number properties)
Reducing to base 2 .. $$2^{4(2x+3)} = 2^{3(x-1)}$$
$$2^{(8x+12)} = 2^{(3x-3)}$$
8x + 12 = 3x - 3 (solving for 'x')
5x = -15
x = -3 'A' is the winner

Bunuel wrote:
If $$16^{2x+3} = 8^{x-1}$$, what is the value of x?

A. -3
B. -1
C. 0
D. 1
E. 3

_________________
Senior Manager
Joined: 16 Feb 2015
Posts: 355
Location: United States
Re: If 16^(2x+3) = 8^(x-1), what is the value of x?  [#permalink]

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20 Dec 2019, 01:03
Bunuel wrote:
If $$16^{2x+3} = 8^{x-1}$$, what is the value of x?

A. -3
B. -1
C. 0
D. 1
E. 3

Explanation:
16^{2x+3} = 8^{x-1}
2^4{2x+3} = 2^3{x-1}
2^{8x+12} = 2^{3x-3}
Equating Power of 2:
8x+12=3x-3
5x=-15
x=-3

IMO-A
Re: If 16^(2x+3) = 8^(x-1), what is the value of x?   [#permalink] 20 Dec 2019, 01:03
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