Last visit was: 20 Jun 2024, 01:55 It is currently 20 Jun 2024, 01:55
Toolkit
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

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.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93832
Own Kudos [?]: 633246 [10]
Given Kudos: 82387
Math Expert
Joined: 02 Sep 2009
Posts: 93832
Own Kudos [?]: 633246 [2]
Given Kudos: 82387
Director
Joined: 25 Apr 2012
Posts: 529
Own Kudos [?]: 2301 [0]
Given Kudos: 740
Location: India
GPA: 3.21
Intern
Joined: 23 Jan 2014
Posts: 14
Own Kudos [?]: 18 [1]
Given Kudos: 0
GMAT 1: 780 Q51 V45
GPA: 4
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink]
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 !

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.
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)
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink]
1
Kudos

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".
Intern
Joined: 23 Jan 2014
Posts: 14
Own Kudos [?]: 18 [0]
Given Kudos: 0
GMAT 1: 780 Q51 V45
GPA: 4
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink]
Quote:

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 )
Manager
Joined: 20 Dec 2013
Posts: 183
Own Kudos [?]: 291 [1]
Given Kudos: 35
Location: India
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink]
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
Intern
Joined: 27 Oct 2011
Posts: 20
Own Kudos [?]: 365 [3]
Given Kudos: 25
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink]
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
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1559
Own Kudos [?]: 7270 [2]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink]
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
Intern
Joined: 03 Aug 2012
Status:Never Give up!!!
Posts: 42
Own Kudos [?]: 103 [1]
Given Kudos: 28
Location: India
Concentration: Finance, General Management
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink]
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)
Manager
Joined: 21 Mar 2011
Status:GMATting
Posts: 96
Own Kudos [?]: 285 [1]
Given Kudos: 104
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink]
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)
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6808
Own Kudos [?]: 30592 [0]
Given Kudos: 799
Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink]
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: $$x = -1$$