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Sub 505 (Easy)|   Exponents|                     
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Bunuel
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If 8^{2x+3}=2^{3x+6}, then x = 17 Feb 2014, 03:37
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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5% (low)

Question Stats:

89% (00:42) correct 11% (00:54) wrong based on 1821 sessions

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

(A) -3
(B) -1
(C) 0
(D) 1
(E) 3
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B
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Bunuel
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If 8^{2x+3}=2^{3x+6}, then x = 17 Feb 2014, 03:37
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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.
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If 8^{2x+3}=2^{3x+6}, then x = 17 Feb 2014, 03:45
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Bunuel

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

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

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
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If 8^{2x+3}=2^{3x+6}, then x = Updated on: 17 Feb 2014, 05:43
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.
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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.
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If 8^{2x+3}=2^{3x+6}, then x = 17 Feb 2014, 05:36
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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".
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If 8^{2x+3}=2^{3x+6}, then x = 17 Feb 2014, 05:42
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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".
Show more

You are perfectly right, answer is indeed B. What a silly mistake ! (that's why you should not try to go too fast :) )
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If 8^{2x+3}=2^{3x+6}, then x = 17 Feb 2014, 09:33
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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

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If 8^{2x+3}=2^{3x+6}, then x = 17 Feb 2014, 12:18
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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
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If 8^{2x+3}=2^{3x+6}, then x = 17 Feb 2014, 19:35
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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
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If 8^{2x+3}=2^{3x+6}, then x = 17 Feb 2014, 22:01
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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)
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If 8^{2x+3}=2^{3x+6}, then x = 18 Feb 2014, 07:22
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(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)
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If 8^{2x+3}=2^{3x+6}, then x = 05 May 2022, 06:08
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Bunuel
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
Show more

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
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If 8^{2x+3}=2^{3x+6}, then x = 23 Apr 2026, 14:20
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