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fitzpratik
Posts: 224
09 Jan 2019, 07:54
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
76% (01:59) correct
24%
(02:20)
wrong
based on 94
sessions
History
Date
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Not Attempted Yet
Given that \(10^\frac{48}{100}\) = x, \(10^\frac{7}{10}\) = y and\(x^z\) = \(y^2\), then the value of z is closest to?
A. 1.45
B. 1.88
C. 2.9
D. 3.7
E. 4.36
A. 1.45
B. 1.88
C. 2.9
D. 3.7
E. 4.36
09 Jan 2019, 08:10
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fitzpratik
GIVEN: \(10^\frac{48}{100}\) = x
Rewrite as: \(10^{0.48}\) = x
GIVEN: \(10^\frac{7}{10}\) = y
Rewrite as: \(10^{0.7}\) = y
GIVEN: \(x^z\) = \(y^2\)
Replace with above values to get: \((10^{0.48})^z\) = \((10^{0.7})^2\)
Apply Power of a Power Law to get: \(10^{0.48z}=10^{1.4}\)
This means: \(0.48z = 1.4\)
Divide both sides by 0.48 to get: \(z = \frac{1.4}{0.48}\)
NOTE: Since \(\frac{1.4}{0.5}=2.8\), we know that \(\frac{1.4}{0.48}\) is a little bit greater than 2.8
Check the answer choices . . .
Answer: C
Cheers,
Brent
KanishkM
Joined: 09 Mar 2018
Last visit: 18 Dec 2021
Posts: 755
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Given Kudos: 123
Location: India
Schools: DeGroote'21 Desautels '21 NUS '21
09 Jan 2019, 08:29
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fitzpratik
I just ball parked in this question.
\(10^\frac{48}{100}\) = x, \(10^\frac{7}{10}\) = y
\(x^z\) = \(y^2\)
\(10^\frac{48}{100}\) = x
\(10^\frac{1}{2}\) = x
\(x^z\) = \(y^2\)
\(10^\frac{z}{2}\) = \(10^\frac{14}{10}\)
\(\frac{z}{2}\)= \(\frac{7}{5}\)
z = 2.85
Answer C
