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# If 9^(2x + 5) = 27^(3x - 10), then x =

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If 9^(2x + 5) = 27^(3x - 10), then x = [#permalink]  20 Nov 2017, 11:36
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Question Stats:

75% (00:23) correct 25% (00:00) wrong based on 8 sessions
If $$9^{(2x + 5)} = 27^{(3x - 10)}$$, then x =

A. 3
B. 6
C. 8
D. 12
E. 15

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[Reveal] Spoiler: OA
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Joined: 10 Apr 2015
Posts: 1169
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Kudos [?]: 1039 [0], given: 6

Re: If 9^(2x + 5) = 27^(3x - 10), then x = [#permalink]  29 Nov 2017, 10:01
Expert's post
Bunuel wrote:
If $$9^{(2x + 5)} = 27^{(3x - 10)}$$, then x =

A. 3
B. 6
C. 8
D. 12
E. 15

First, we need a COMMON BASE
Here, that common base will be 3 (since we can rewrite 9 and 27 as powers of 3)

Give: 9^(2x + 5) = 27^(3x - 10)
Rewrite bases as follows: (3²)^(2x + 5) = (3³)^(3x - 10)
Apply Power of a Power rule to get: 3^(4x + 10) = 3^(9x - 30)
So, (4x + 10) = (9x - 30)
Add 30 to both sides: 4x + 40 = 9x
Subtract 4x from both sides: 40 = 5x
Solve: x = 8

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Re: If 9^(2x + 5) = 27^(3x - 10), then x =   [#permalink] 29 Nov 2017, 10:01
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