BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

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

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Thu Oct 01, 2020 9:01 am

Re: If \(9^{2x+5}=27^{3x-10},\) then \(x =\)

by Chandanagarwal » Thu Oct 01, 2020 9:08 am
2(2x+5) = 3(3x-10)

4x+10 = 9x -30

5x = 40

x=8
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 24
Joined: Wed Jun 29, 2011 1:47 am

Re: If \(9^{2x+5}=27^{3x-10},\) then \(x =\)

by psarma » Thu Oct 01, 2020 3:27 pm
\(9^{2x+5}\) = \(3^{2\left(2x+5\right)}\)
= \(3^{4x+10}\)
Likewise,
\(27^{3x-10}\) = \(3^{3\left(3x-10\right)}\)
= \(3^{9x-30}\)

Equating the powers together;
4x+10 = 9x-30
i.e 5x=40
or x=8
Answer C
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8155
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

Re: If \(9^{2x+5}=27^{3x-10},\) then \(x =\)

by Scott@TargetTestPrep » Tue Oct 06, 2020 3:18 am
Gmat_mission wrote: ↑
Thu Oct 01, 2020 7:04 am
 If \(9^{2x+5}=27^{3x-10},\) then \(x =\)

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

Answer: C

Solution:

We first must get a base of 3 for each expression so that we can then equate the exponents. Simplifying, we have:

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

3^(4x + 10) = 3^(9x - 30)

4x + 10 = 9x - 30

40 = 5x

8 = x

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1