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

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Math Expert
Joined: 02 Sep 2009
Posts: 53067
If 9^(2x + 5) = 27^(3x − 10), then x =  [#permalink]

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18 Oct 2018, 01:21
00:00

Difficulty:

15% (low)

Question Stats:

86% (01:12) correct 14% (01:30) wrong based on 34 sessions

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If $$9^{(2x + 5)} = 27^{(3x − 10)}$$, then x =

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

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Posts: 3343
Location: India
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If 9^(2x + 5) = 27^(3x − 10), then x =  [#permalink]

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18 Oct 2018, 01:31
Bunuel wrote:
If $$9^{(2x + 5)} = 27^{(3x − 10)}$$, then x =

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

Formula used: $$(a^m)^n = a^{m*n}$$

In this problem, the first step is to bring both sides to have the same base

$$9^{(2x + 5)} = 27^{(3x − 10)}$$ -> $$(3^2)^{(2x + 5)} = (3^3)^{(3x − 10)}$$ -> $$3^{4x + 10} = 3^{9x - 30}$$

Therefore, we have $$4x + 10 = 9x - 30$$ -> $$5x = 40$$ -> $$x =$$ 8(Option C)
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Joined: 08 Oct 2018
Posts: 7
Re: If 9^(2x + 5) = 27^(3x − 10), then x =  [#permalink]

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18 Oct 2018, 02:43
3
Bunuel wrote:
If $$9^{(2x + 5)} = 27^{(3x − 10)}$$, then x =

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

9^{2x+5}=3^2{2x+5}
27^{3x-10}=3^3{3x-10}
equating them ,we see bases are same so the powers would be equated
4x+10=9x-30
solving for x=8
Re: If 9^(2x + 5) = 27^(3x − 10), then x =   [#permalink] 18 Oct 2018, 02:43
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