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# If 16^(x + 7) = 2^(6x + 18), what is x?

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Math Expert
Joined: 02 Sep 2009
Posts: 62499
If 16^(x + 7) = 2^(6x + 18), what is x?  [#permalink]

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05 Sep 2019, 02:36
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15% (low)

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95% (00:36) correct 5% (00:59) wrong based on 22 sessions

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If $$16^{x + 7} = 2^{6x + 18}$$, what is x?

A. 9
B. 8
C. 7
D. 6
E. 5

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Re: If 16^(x + 7) = 2^(6x + 18), what is x?  [#permalink]

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05 Sep 2019, 05:19
Bunuel wrote:
If $$16^{x + 7} = 2^{6x + 18}$$, what is x?

A. 9
B. 8
C. 7
D. 6
E. 5

equate
4x+28=6x+18
x=5
IMO E
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Re: If 16^(x + 7) = 2^(6x + 18), what is x?  [#permalink]

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08 Sep 2019, 10:14
Bunuel wrote:
If $$16^{x + 7} = 2^{6x + 18}$$, what is x?

A. 9
B. 8
C. 7
D. 6
E. 5

For this exponential equation, we must first obtain like bases, and then we can equate the exponents. We note that 16 = 2^4, and we have:

(2^4)^(x+7) = 2^(6x+18)

2^(4x+28) = 2^(6x+18)

4x + 28 = 6x + 18

10 = 2x

5 = x

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Re: If 16^(x + 7) = 2^(6x + 18), what is x?   [#permalink] 08 Sep 2019, 10:14
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