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Founder  Joined: 18 Apr 2015
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If 9^2X+5 [#permalink]
Expert's post 00:00

Question Stats: 90% (00:34) correct 10% (01:00) wrong based on 10 sessions
If $$9^{2x+5} = 27^{3x-10}$$, then x=

A. 3

B. 6

C. 8

D. 12

E. 15
[Reveal] Spoiler: OA

_________________ GRE Instructor Joined: 10 Apr 2015
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Re: If 9^2X+5 [#permalink]
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Expert's post
Carcass wrote:
If $$9^{2x+5} = 27^{3x-10}$$, then x=

A. 3

B. 6

C. 8

D. 12

E. 15

Rewrite each side with the SAME BASE.

So, we can replace 9 with 3², and replace 27 with 3³ to get: $$(3²)^{2x+5} = (3³)^{3x-10}$$

Apply the Power of a Power law to get: $$3^{4x+10} = 3^{9x-30}$$

This means that $$4x+10=9x-30$$

Add 30 to both sides to get: $$4x+40=9x$$

Subtract 4x from both sides to get: $$40=5x$$

Solve: x = 8

Answer: C

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Intern Joined: 07 Aug 2016
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Re: If 9^2X+5 [#permalink]
Carcass wrote:
If $$9^{2x+5} = 27^{3x-10}$$, then x=

A. 3

B. 6

C. 8

D. 12

E. 15

3^2(2x + 5) = 3^3(3x - 10)

4x + 10 = 9x - 30

-5x = -40
x = 8
Manager Joined: 23 Oct 2018
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Re: If 9^2X+5 [#permalink]
thanks Re: If 9^2X+5   [#permalink] 27 Nov 2018, 06:54
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