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 →

Equations with variables in the exponents

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Quantitative Reasoning |
Master | Next Rank: 500 Posts
Posts: 363
Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members
Thanked: 115 times

by theCEO » Wed Jun 20, 2012 9:31 pm
5^21 * 4^11 = 2 * 10^n
5(5^20) * 4(4^10) = 2 * 10^n
(5^20) * (4^10) = 0.1 * 10^n
(5^10) * (5^10)* (4^10) = 0.1 * 10^n
(5*5*4)^10 = 0.1 * 10^n
100^10 = 0.1 * 10^n
10^20 = 10^-1 * 10^n
10^21 = 10^n
n = 21
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 363
Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members
Thanked: 115 times

by theCEO » Wed Jun 20, 2012 9:43 pm
2^x - 2^x-2 = 3(2^13)
2^x - (2^x * 2^-2) = 3(2^13)
2^x(1-2^-2) = 3(2^13)
2^x(1-0.25) = 3(2^13)
2^x(3/4) = 3(2^13)
2^x = 3(2^13) * (4/3)
2^x = 4*(2^13)
2^x = 2^2*(2^13)
2^x = 2^15
x = 15
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 768
Joined: Wed Dec 28, 2011 4:18 pmFollowed by: 140 members
Location: Berkeley, CA
Thanked: 387 times

by Mike@Magoosh » Thu Jun 21, 2012 4:10 pm
Kim9876Zey wrote:I think I am missing some of the rules in solving these
Dear Kim9876Zey

You might find this blog article a helpful summary of the laws of exponents.
https://magoosh.com/gmat/2012/exponent-p ... -the-gmat/

Here's a somewhat related practice question:
https://gmat.magoosh.com/admin/questions/913
When you submit your answer, the following page will have the complete video solution.

Let me know if you have any further questions.

Mike :)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Junior | Next Rank: 30 Posts
Posts: 19
Joined: Thu Jun 21, 2012 6:55 pm
Thanked: 5 times

by jcnasia » Fri Jun 22, 2012 7:06 am
You can also solve this problem by taking the log of both sides.
log(5^21 * 4^11) = log(2 * 10^n)

21 * log 5 + 11 * log 4 = log 2 + n * log 10
21 * log 5 + 11 * 2 * log 2 - log 2 = n
21 * log 5 + 21 * log 2 = n
21 * log(5*2) = n
21 = n
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1