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Which of the following options should be the least value of
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15 Oct 2015, 10:30
15 Oct 2015, 10:30
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74% (01:30) correct
25% (01:10) wrong based on 31 sessions
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Which of the following options should be the least value of n that satisfies the inequality, \(2^n > (10^{15})\) ?
A. 30
B. 45
C. 60
D. 75
E. 90
and the right answer is 60
please explain as I could not even get the sense on how to start solving it.
A. 30
B. 45
C. 60
D. 75
E. 90
and the right answer is 60
please explain as I could not even get the sense on how to start solving it.
Re: Inequalities
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09 Oct 2017, 20:04
09 Oct 2017, 20:04
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1
(2)^n > 10^15
\divide the powers by n
2 > 10^(15/n)
if n = 30
2 < 10^(15/30)
2 < sqrt(10)
which is incorrect.
if n = 45
2 < 10^(15/45)
2 < cuberoot(10)
which is incorrect.
if n = 60
2 > 10^(15/60)
2 > (10)^(1/4).
therefore least value of n = 60.
\divide the powers by n
2 > 10^(15/n)
if n = 30
2 < 10^(15/30)
2 < sqrt(10)
which is incorrect.
if n = 45
2 < 10^(15/45)
2 < cuberoot(10)
which is incorrect.
if n = 60
2 > 10^(15/60)
2 > (10)^(1/4).
therefore least value of n = 60.
Re: Inequalities
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14 Oct 2017, 23:46
14 Oct 2017, 23:46
3
Sujan Sareen wrote:
Which of the following options should be the least value of n that satisfies the inequality, 2^n > (10^15) ?
options are:
30
45
60
75
90
and the right answer is 60
please explain as I could not even get the sense on how to start solving it.
options are:
30
45
60
75
90
and the right answer is 60
please explain as I could not even get the sense on how to start solving it.
2^10 >10^3
Now write
(2^10)^5 > (10^3)^5
The answer should be 50. 45 makes it less, so choose 60.
