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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If 3^{6x-3} = 2/3, then 3^(3x)
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04 Jul 2022, 08:08
04 Jul 2022, 08:08
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Question Stats:
90% (01:26) correct
10% (02:26) wrong based on 10 sessions
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If \(3^{6x-3} = \frac{2}{3}\), then \(3^{3x} = \)
(A) \(6\sqrt{2}\)
(B) \(6\sqrt{3}\)
(C) \(2\sqrt{6}\)
(D) \(2\sqrt{3}\)
(E) \(3\sqrt{2}\)
(A) \(6\sqrt{2}\)
(B) \(6\sqrt{3}\)
(C) \(2\sqrt{6}\)
(D) \(2\sqrt{3}\)
(E) \(3\sqrt{2}\)
Re: If 3^{6x-3} = 2/3, then 3^(3x)
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05 Jul 2022, 03:48
05 Jul 2022, 03:48
1
This one is tough but I solved it as follows.
3^{6x-3} = 2*3^-1
3^{6x}*3^-3 = 2*3^-1
3^{6x-2}*3^-1 = 2*3^-1
3^{6x-2} = 2
3^(3x)*3^(3x)*3^(-2) = 2
[3^(3x)*3^(3x)*3]/9 = 2
From here I plugged in the answer choices to figure out which one satisfied the equation.
Answer is E
3^{6x-3} = 2*3^-1
3^{6x}*3^-3 = 2*3^-1
3^{6x-2}*3^-1 = 2*3^-1
3^{6x-2} = 2
3^(3x)*3^(3x)*3^(-2) = 2
[3^(3x)*3^(3x)*3]/9 = 2
From here I plugged in the answer choices to figure out which one satisfied the equation.
Answer is E
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If 3^{6x-3} = 2/3, then 3^(3x)
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05 Jul 2022, 07:21
05 Jul 2022, 07:21
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GreenlightTestPrep wrote:
If \(3^{6x-3} = \frac{2}{3}\), then \(3^{3x} = \)
(A) \(6\sqrt{2}\)
(B) \(6\sqrt{3}\)
(C) \(2\sqrt{6}\)
(D) \(2\sqrt{3}\)
(E) \(3\sqrt{2}\)
(A) \(6\sqrt{2}\)
(B) \(6\sqrt{3}\)
(C) \(2\sqrt{6}\)
(D) \(2\sqrt{3}\)
(E) \(3\sqrt{2}\)
Here's another approach...
Given: \(3^{6x-3} = \frac{2}{3}\)
For the left side, use the Quotient rule in reverse to get: \(\frac{3^{6x}}{3^{3}} = \frac{2}{3}\)
Evaluate then denominator to get: \(\frac{3^{6x}}{27} = \frac{2}{3}\)
Multiply both sides of the equation by \(27\) to get: \(3^{6x} = 18\)
Raise both sides to the power of \(\frac{1}{2}\) to get: \((3^{6x})^{\frac{1}{2}} = 18^{\frac{1}{2}}\)
Simplify: \(3^{3x} = \sqrt{18} = (\sqrt{9})(\sqrt{2}) = 3\sqrt{2}\)
Answer: E
