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28 Jan 2019, 02:43
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C
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Difficulty:
65%
(hard)
Question Stats:
62% (02:24) correct
38%
(02:07)
wrong
based on 923
sessions
History
Date
Time
Result
Not Attempted Yet
If \(\sqrt{\sqrt{\sqrt{5x}}} = \sqrt[6]{4x}\), what is the range of the possible values of x?
A. 0
B. 1/4
C. 125/256
D. 1/2
E. 131/256
M37-65
A. 0
B. 1/4
C. 125/256
D. 1/2
E. 131/256
M37-65
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30 Nov 2021, 04:07
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Official Solution:
If \(\sqrt{\sqrt{\sqrt{5x}}} = \sqrt[6]{4x}\), what is the range of the possible values of \(x\)?
A. \(0\)
B. \(\frac{1}{4}\)
C. \(\frac{125}{256}\)
D. \(\frac{1}{2}\)
E. \(\frac{131}{256}\)
\(\sqrt{\sqrt{\sqrt{5x}}} = \sqrt[6]{4x}\);
\((5x)^{\frac{1}{2}*\frac{1}{2}*\frac{1}{2}} =(4x)^{\frac{1}{6}}\);
\((5x)^{\frac{1}{8}} =(4x)^{\frac{1}{6}}\);
Take to the power of 24 (the LCM of 8 and 6): \((5x)^3 =(4x)^4\);
\(x^3(256x-125)=0\);
\(x=0\) or \(x=\frac{125}{256}\).
The range of the possible values of \(x\) is therefore \(\frac{125}{256}-0=\frac{125}{256}\).
Answer: C
If \(\sqrt{\sqrt{\sqrt{5x}}} = \sqrt[6]{4x}\), what is the range of the possible values of \(x\)?
A. \(0\)
B. \(\frac{1}{4}\)
C. \(\frac{125}{256}\)
D. \(\frac{1}{2}\)
E. \(\frac{131}{256}\)
\(\sqrt{\sqrt{\sqrt{5x}}} = \sqrt[6]{4x}\);
\((5x)^{\frac{1}{2}*\frac{1}{2}*\frac{1}{2}} =(4x)^{\frac{1}{6}}\);
\((5x)^{\frac{1}{8}} =(4x)^{\frac{1}{6}}\);
Take to the power of 24 (the LCM of 8 and 6): \((5x)^3 =(4x)^4\);
\(x^3(256x-125)=0\);
\(x=0\) or \(x=\frac{125}{256}\).
The range of the possible values of \(x\) is therefore \(\frac{125}{256}-0=\frac{125}{256}\).
Answer: C
General Discussion
KanishkM
Joined: 09 Mar 2018
Last visit: 18 Dec 2021
Posts: 759
Given Kudos: 123
Location: India
Schools: DeGroote'21 Desautels '21 NUS '21
28 Jan 2019, 03:09
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Bunuel
5x ^ 1/8 = 4x^1/6
Multiplying both powers by 24
{5x}^3 = {\(2^2\) * x} ^4
{2^2 * x} ^ 4 - {5x}^3 = 0
x^3 ( 256 x - 125) = 0
Range = HT - LT
125/256 - 0
C
