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If (25^(1/3))^x = 5, then x =
[#permalink]
13 Jan 2022, 09:11
13 Jan 2022, 09:11
Expert Reply
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Question Stats:
77% (00:39) correct
22% (00:43) wrong based on 9 sessions
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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If (25^(1/3))^x = 5, then x =
[#permalink]
13 Jan 2022, 10:55
13 Jan 2022, 10:55
Carcass wrote:
If \((\sqrt[3]{25})^x=5\), then x=
A. 6
B. 3
C. 3/2
D. 2/3
E. 3/5
A. 6
B. 3
C. 3/2
D. 2/3
E. 3/5
Important property: \((\sqrt[a]{k})^b=k^{\frac{b}{a}}\)
Given: \((\sqrt[3]{25})^x=5\)
Apply property to get: \(25^{\frac{x}{3}}=5\)
Rewrite both sides as follows: \((5^2)^{\frac{x}{3}}=5^1\)
Apply Power of a Power law to left side: \(5^{\frac{2x}{3}}=5^1\)
Since the bases both equal 5, we can conclude that \(\frac{2x}{3}=1\)
Multiply both sides by \(3\) to get: \(2x = 3\)
Divide both sides by \(2\) to get: \(x = \frac{3}{2}\)
Answer: C
Cheers,
Brent
gmatclubot
Re: If (25^(1/3))^x = 5, then x = [#permalink]
13 Jan 2022, 10:55
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