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

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

Posted from my mobile device
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Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink]
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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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Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink]
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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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Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink]
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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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Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink]
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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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Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink]
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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
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Re: If 8^{2x+3}=2^{3x+6}, then x = [#permalink]
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