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If 8^{2x+3}=2^{3x+6}, then x =
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10 Jul 2020, 07:58
10 Jul 2020, 07:58
Expert Reply
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Question Stats:
87% (00:30) correct
12% (00:43) wrong based on 24 sessions
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Re: If 8^{2x+3}=2^{3x+6}, then x =
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10 Jul 2020, 07:58
10 Jul 2020, 07:58
Expert Reply
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Re: If 8^{2x+3}=2^{3x+6}, then x =
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06 May 2022, 07:43
06 May 2022, 07:43
1
Carcass wrote:
If \(8^{2x+3}=2^{3x+6}\), then x =
(A) -3
(B) -1
(C) 0
(D) 1
(E) 3
(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
