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If \sqrt27=3^m
[#permalink]
17 Apr 2019, 01:44
17 Apr 2019, 01:44
Expert Reply
00:00
Question Stats:
85% (00:39) correct
14% (00:43) wrong based on 14 sessions
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If \(\sqrt[m]{27}=3^{3m}\) and \(4^m > 1\), then what is the value of m ?
A. \(-1\)
B. \(- \frac{1}{4}\)
C. \(0\)
D. \(\frac{1}{4}\)
E. \(1\)
A. \(-1\)
B. \(- \frac{1}{4}\)
C. \(0\)
D. \(\frac{1}{4}\)
E. \(1\)
Re: If \sqrt27=3^m
[#permalink]
21 Apr 2019, 05:04
21 Apr 2019, 05:04
1
from question
\(27\frac{^1^}{^m} = 3^3^m\)
or, \(3\frac{^3}{m} = 3^3^m\)
or, \(\frac{3}{m} = 3m\)
or, \(3 = 3m^2\)
or, \(1 = m^2\)
therefore \(m = +1 or -1\)
however \(4^m > 1\) so \(m =1\)
\(27\frac{^1^}{^m} = 3^3^m\)
or, \(3\frac{^3}{m} = 3^3^m\)
or, \(\frac{3}{m} = 3m\)
or, \(3 = 3m^2\)
or, \(1 = m^2\)
therefore \(m = +1 or -1\)
however \(4^m > 1\) so \(m =1\)
gmatclubot
Re: If \sqrt27=3^m [#permalink]
21 Apr 2019, 05:04
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