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If 5*125^(1/x) = 1/(5^(1/x)), then x = ?
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08 Mar 2021, 11:06
08 Mar 2021, 11:06
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If \(5*\sqrt[x]{125}=\frac{1}{5^{\frac{1}{x}}}\), then x = ?
A. -4
B. \(\frac{-1}{\sqrt{2}}\)
C. 0
D. \(\frac{1}{\sqrt{2}}\)
E. 1
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. -4
B. \(\frac{-1}{\sqrt{2}}\)
C. 0
D. \(\frac{1}{\sqrt{2}}\)
E. 1
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Joined: 10 Apr 2015
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Re: If 5*125^(1/x) = 1/(5^(1/x)), then x = ?
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08 Mar 2021, 12:33
08 Mar 2021, 12:33
1
Carcass wrote:
If \(5*\sqrt[x]{125}=\frac{1}{5^{\frac{1}{x}}}\), then x = ?
A. -4
B. \(\frac{-1}{\sqrt{2}}\)
C. 0
D. \(\frac{1}{\sqrt{2}}\)
E. 1
A. -4
B. \(\frac{-1}{\sqrt{2}}\)
C. 0
D. \(\frac{1}{\sqrt{2}}\)
E. 1
\(\sqrt[x]{125}\) = 125^(1/x)
= (5^3)^(1/x)
= 5^(3/x)
So, \(5*\sqrt[x]{125}\) = (5^1)[5^(3/x)] = 5^(3/x + 1)
RULE: b^(-x) = 1/(b^x)
So, \(\frac{1}{5^{\frac{1}{x}}}\) = 5^(-1/x)
Given: \(5*\sqrt[x]{125}=\frac{1}{5^{\frac{1}{x}}}\)
We get: 5^(3/x + 1) = 5^(-1/x)
Since the bases are equal, we can conclude: 3/x + 1 = -1/x
Multiply both sides by x to get: 3 + x = -1
Solve: x = -4
Answer: A
General Discussion
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Status:Founder & Quant Trainer
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If 5*125^(1/x) = 1/(5^(1/x)), then x = ?
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08 Mar 2021, 23:12
08 Mar 2021, 23:12
Carcass wrote:
If \(5*\sqrt[x]{125}=\frac{1}{5^{\frac{1}{x}}}\), then x = ?
A. -4
B. \(\frac{-1}{\sqrt{2}}\)
C. 0
D. \(\frac{1}{\sqrt{2}}\)
E. 1
A. -4
B. \(\frac{-1}{\sqrt{2}}\)
C. 0
D. \(\frac{1}{\sqrt{2}}\)
E. 1
\(5*\sqrt[x]{125}=\frac{1}{5^{\frac{1}{x}}}\)
\((5)5^{\frac{3}{x}} = 5^{\frac{-1}{x}}\)
\(5^{\frac{3}{x} + 1} = 5^{\frac{-1}{x}}\)
When the bases are equal, powers are also equal;
\(\frac{3}{x} + 1 = \frac{-1}{x}\)
\(\frac{4}{x} = -1\)
\(x = -4\)
Hence, option A
