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If √√√(3x) = 4√(2x), what is the greatest possible value of
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Bunuel
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If √√√(3x) = 4√(2x), what is the greatest possible value of [#permalink] New post  21 Nov 2017, 00:55
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If \(\sqrt{\sqrt{\sqrt{3x}}} = \sqrt[4]{2x}\), what is the greatest possible value of x?


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priteshsad
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Re: If √√√(3x) = 4√(2x), what is the greatest possible value of [#permalink] New post  24 Nov 2017, 22:41
2/9 ?
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bikachu
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Re: If √√√(3x) = 4√(2x), what is the greatest possible value of [#permalink] New post  25 Nov 2017, 01:15
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priteshsad wrote:
2/9 ?


Nope. The question comes down to (3x)^ 1/6 = (2x) ^ 1/4

so 3x = (2x) ^6/4 or (2x)^2
3x = 4x^2
x = 3/4
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Gawain
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Re: If √√√(3x) = 4√(2x), what is the greatest possible value of [#permalink] New post  07 Dec 2017, 20:40
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it stands for (3x)^ 1/8 = (2x) ^ 1/4 ,
so 3x=(2x)^1/2,
3x=4*x^2
x=3/4
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Re: If √√√(3x) = 4√(2x), what is the greatest possible value of [#permalink] New post  17 Oct 2021, 07:18
could someone explain in more detail?
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If √√√(3x) = 4√(2x), what is the greatest possible value of [#permalink] New post  17 Oct 2021, 07:48
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\(3x^{\frac{1}{8}}= 2x^{\frac{1}{4}}\)

When both sides are raised to the fourth power

\(\sqrt{3x} = 2x\)

Squaring both the sides

\(3x = 4x^2\)

\(4x^2 - 3x = 0\)

\(x(x - \frac{3}{4}) = 0\)

\(x = 0 / \frac{3}{4}\)

Greatest possible value \(= \frac{3}{4}\)

Samamammadova8888 wrote:
could someone explain in more detail?

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samkerrvnw
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Re: If √√√(3x) = 4√(2x), what is the greatest possible value of [#permalink] New post  22 Oct 2021, 08:00
Thanks for the explanation!
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