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If x = 101.4, y = 100.7, and xz = y3, then what is the value
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16 Apr 2019, 00:38
16 Apr 2019, 00:38
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Question Stats:
82% (01:14) correct
17% (01:20) wrong based on 39 sessions
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If \(x = 10^{1.4}\), \(y = 10^{0.7}\), and \(x^z = y^3\), then what is the value of \(z\) ?
(A) 0.5
(B) 0.66
(C) 1.5
(D) 2
(E) 3
(A) 0.5
(B) 0.66
(C) 1.5
(D) 2
(E) 3
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Joined: 10 Apr 2015
Posts: 6218
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If x = 101.4, y = 100.7, and xz = y3, then what is the value
[#permalink]
16 Apr 2019, 08:09
16 Apr 2019, 08:09
Carcass wrote:
If \(x = 10^{1.4}\), \(y = 10^{0.7}\), and \(x^z = y^3\), then what is the value of \(z\) ?
(A) 0.5
(B) 0.66
(C) 1.5
(D) 2
(E) 3
(A) 0.5
(B) 0.66
(C) 1.5
(D) 2
(E) 3
GIVEN: \(x^z = y^3\)
When we replace \(x\) with \(10^{1.4}\), and \(y\) with \(10^{0.7}\), we get: \((10^{1.4})^z = (10^{0.7})^3\)
Simplify to get: \(10^{1.4z} = 10^{2.1}\)
This means: \(1.4z = 2.1\)
Solve: \(z = \frac{2.1}{1.4}=\frac{21}{14}=\frac{3}{2}=1.5\)
Answer: C
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If x = 101.4, y = 100.7, and xz = y3, then what is the value [#permalink]
16 Apr 2019, 08:09
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