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18 Nov 2019, 00:19
Kudos
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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:
75%
(hard)
Question Stats:
54% (02:12) correct
46%
(02:29)
wrong
based on 227
sessions
History
Date
Time
Result
Not Attempted Yet
If \(2^{10}≒10^3\) and \(5^{20}≒10^x\), then what is the value of integer \(x\)?
A. \(10\)
B. \(12\)
C. \(14\)
D. \(16\)
E. \(18\)
A. \(10\)
B. \(12\)
C. \(14\)
D. \(16\)
E. \(18\)
18 Nov 2019, 09:36
Kudos
Bookmarks
Multiply both sides of the eq 5^20=10^x by 2^20
5^20 . 2^20= 10^x . 2^20
10^20=10^x .2^20
Subst other eq
10^20=10^x. 10^6
20=x+6
X=14
Posted from my mobile device
5^20 . 2^20= 10^x . 2^20
10^20=10^x .2^20
Subst other eq
10^20=10^x. 10^6
20=x+6
X=14
Posted from my mobile device
General Discussion
18 Nov 2019, 05:32
Kudos
Bookmarks
MathRevolution
This is what the question is meant to be
\(2^{10}≒10^3=2^35^3......2^32^7=2^35^3.....2^7=5^3........5=2^\frac{7}{3}\).....
\(5^{20}≒10^x.........5^{20}=(2^{\frac{7}{3}})^{20}=2^{20*\frac{7}{3}}=10^x=2^x5^x=2^x2^{\frac{7x}{3}}...........\frac{140}{3}=x+\frac{7x}{3}=\frac{10x}{3}.....x=\frac{140*3}{10*3}=14\)
C
