Last visit was: 26 Jul 2024, 17:10 It is currently 26 Jul 2024, 17:10
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If 8^{2x+3}=2^{3x+6}, then x =

SORT BY:
Date
Kudos
Tags:
Difficulty: Sub 505 Level,   Exponents,                     
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 94619
Own Kudos [?]: 644160 [10]
Given Kudos: 86770
Send PM
CAT Tests Forum Quiz Mode
If 8^{2x+3}=2^{3x+6}, then x = [#permalink] If 8^{2x+3}=2^{3x+6}, then x =   17 Feb 2014, 03:37
2
Kudos
8
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

87% (00:42) correct 13% (00:51) wrong based on 1399 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
If \(8^{2x+3}=2^{3x+6}\), then x =

(A) -3
(B) -1
(C) 0
(D) 1
(E) 3
ShowHide Answer
Official Answer
B
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 94619
Own Kudos [?]: 644160 [2]
Given Kudos: 86770
Send PM
CAT Tests Forum Quiz Mode
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink] If 8^{2x+3}=2^{3x+6}, then x =   17 Feb 2014, 03:37
1
Kudos
1
Bookmarks
Expert Reply
SOLUTION

If \(8^{2x+3}=2^{3x+6}\), then x =

(A) -3
(B) -1
(C) 0
(D) 1
(E) 3

\(8^{2x+3}=2^{3x+6}\);

\(2^{3(2x+3)}=2^{3x+6}\);

Equate the powers of the same bases: \(3(2x+3)=3x+6\) --> \(x=-1\).

Answer: B.
User avatar
WoundedTiger
Director
Director
Joined: 25 Apr 2012
Posts: 529
Own Kudos [?]: 2324 [0]
Given Kudos: 740
Location: India
GPA: 3.21
WE:Business Development (Other)
Send PM
Reviews Badge
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink] If 8^{2x+3}=2^{3x+6}, then x =   17 Feb 2014, 03:45
Bunuel wrote:
If \(8^{2x+3}=2^{3x+6},\) then x =

(A) -3
(B) -1
(C) 0
(D) 1
(E) 3


Sol: The expression can be re-written as 2^3(2x+3)=2^(3x+6). Equating the powers we get

3(2x+3)=3x+6
6x+9=3x+6 or x=1

Ans D

600 level is okay
avatar
GMarc
Intern
Intern
Joined: 23 Jan 2014
Posts: 14
Own Kudos [?]: 18 [1]
Given Kudos: 0
GMAT 1: 780 Q51 V45
GPA: 4
Send PM
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink] If 8^{2x+3}=2^{3x+6}, then x =   Updated on: 17 Feb 2014, 05:43
1
Kudos
Since \(8 = 2^3\) we can write \(2^{3(2x+3)} = 2^{3x+6)}\) and then \(3(2x+3) = 3x+6\) so that \(3x = 3\) and x = 1 !

Answer is D

EDIT : well actually \(3(2x+3) = 3x+6\) then \(3x = -3\) and x = -1.

Originally posted by GMarc on 17 Feb 2014, 03:46.
Last edited by GMarc on 17 Feb 2014, 05:43, edited 1 time in total.
User avatar
Abdul29
Manager
Manager
Joined: 11 Jan 2014
Posts: 78
Own Kudos [?]: 413 [1]
Given Kudos: 11
Concentration: Finance, Statistics
GMAT Date: 03-04-2014
GPA: 3.77
WE:Analyst (Retail Banking)
Send PM
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink] If 8^{2x+3}=2^{3x+6}, then x =   17 Feb 2014, 05:36
1
Kudos
You guys made me question my answer, several times. :P

I got (B).

After equalizing both bases (since 8= \(2^3\)), we also equalize exponents:

3(2x+3) = 3x+6, results in x being "-1" not "1".
avatar
GMarc
Intern
Intern
Joined: 23 Jan 2014
Posts: 14
Own Kudos [?]: 18 [0]
Given Kudos: 0
GMAT 1: 780 Q51 V45
GPA: 4
Send PM
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink] If 8^{2x+3}=2^{3x+6}, then x =   17 Feb 2014, 05:42
Quote:
You guys made me question my answer, several times.

I got (B).

After equalizing both bases (since 8= ), we also equalize exponents:

3(2x+3) = 3x+6, results in x being "-1" not "1".


You are perfectly right, answer is indeed B. What a silly mistake ! (that's why you should not try to go too fast :) )
avatar
B
AKG1593
Manager
Manager
Joined: 20 Dec 2013
Posts: 183
Own Kudos [?]: 293 [1]
Given Kudos: 35
Location: India
Send PM
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink] If 8^{2x+3}=2^{3x+6}, then x =   17 Feb 2014, 09:33
1
Kudos
Was stumped to see D chosen by some usually correct people here.
Choosing Option B
8^(2x+3)=2^[3(2x+3)]=LHS
RHS=3(x+2)
Equating:2x+3=x+2
X=-1

Posted from my mobile device
User avatar
djanand
Intern
Intern
Joined: 27 Oct 2011
Posts: 20
Own Kudos [?]: 367 [3]
Given Kudos: 25
Send PM
GMAT ToolKit User
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink] If 8^{2x+3}=2^{3x+6}, then x =   17 Feb 2014, 12:18
3
Kudos
Another method is to substitute the answer options in the question.

A) put x= -3, 8^{-3} = 2^{-3}
B) put x= -1 , 8^{1} = 2^{3} ----- Correct
C) put x= 0, 8^{3} = 2 ^{6}
D) put x =1 , 8^{5} = 2^{9}
E) put x=3, 8^{9} = 2^{15}

Option B
avatar
PareshGmat
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1558
Own Kudos [?]: 7304 [2]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink] If 8^{2x+3}=2^{3x+6}, then x =   17 Feb 2014, 19:35
2
Kudos
One more method:
Re-writing equation as
8 ^ (2x+3) = 8 ^ 1/3(3x+6)
8 ^ (2x+3) = 8 ^ (x+2)

Equating the powers

2x+3 = x+2
x=-1 Answer = B
User avatar
Manofsteel
Intern
Intern
Joined: 03 Aug 2012
Status:Never Give up!!!
Posts: 42
Own Kudos [?]: 103 [1]
Given Kudos: 28
Location: India
Concentration: Finance, General Management
Send PM
GMAT ToolKit User
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink] If 8^{2x+3}=2^{3x+6}, then x =   17 Feb 2014, 22:01
1
Kudos
Pretty easy:-
Get both sides to the same base i.e 2
so 8 gets converted to 2^3
Now since bases are same equate the powers
3(2x+3)=3x+6
Solve the above you get x=-1. Option(B)
User avatar
nutshell
Manager
Manager
Joined: 21 Mar 2011
Status:GMATting
Posts: 96
Own Kudos [?]: 288 [1]
Given Kudos: 104
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
Send PM
GMAT ToolKit User
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink] If 8^{2x+3}=2^{3x+6}, then x =   18 Feb 2014, 07:22
1
Kudos
(2^3)^{2x+3} = 2^{3x+6}
2^{6x+9} = 2^{3x+6}
Equate the powers: 6x+9 = 3x+6;
3x = -3;
x = -1;

Ans is (B)
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30868 [0]
Given Kudos: 799
Location: Canada
Send PM
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink] If 8^{2x+3}=2^{3x+6}, then x =   05 May 2022, 06:08
Expert Reply
Top Contributor
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If \(8^{2x+3}=2^{3x+6}\), then x =

(A) -3
(B) -1
(C) 0
(D) 1
(E) 3


To solve this question, we must first rewrite one or more of the expressions so they have the same base

We can do this by replacing \(8\) with \(2^3\) to get: \((2^3)^{2x+3}=2^{3x+6}\)

Now apply the power of a power law to the left side to get: \(2^{6x+9}=2^{3x+6}\)

Now that we have the same bases, we know the exponents must be equal: \(6x+9=3x+6\)

Subtract \(3x\) from both sides of the equation: \(3x+9=6\)

Subtract \(9\) from both sides of the equation: \(3x=-3\)

Divide both sides by \(3\) to get: \(x = -1\)

Answer: B
GMAT Club Bot
gmatclubot
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink]
05 May 2022, 06:08
Moderator:
Bunuel
Math Expert
94619 posts