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If (5^sqrtof2)^m=25
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04 Aug 2021, 06:48
04 Aug 2021, 06:48
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Question Stats:
91% (00:33) correct
8% (00:55) wrong based on 23 sessions
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If \((5^{\sqrt{2}})^m=25\), what is the value of m?
A. \(-2\)
B. \(- \sqrt{2}\)
C. \(\sqrt{2}\)
D. \(2\)
E. \(2 \sqrt{2} \)
A. \(-2\)
B. \(- \sqrt{2}\)
C. \(\sqrt{2}\)
D. \(2\)
E. \(2 \sqrt{2} \)
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If (5^sqrtof2)^m=25
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04 Aug 2021, 06:54
04 Aug 2021, 06:54
1
Carcass wrote:
If \((5^{\sqrt{2}})^m=25\), what is the value of m?
A. \(-2\)
B. \(- \sqrt{2}\)
C. \(\sqrt{2}\)
D. \(2\)
E. \(2 \sqrt{2} \)
A. \(-2\)
B. \(- \sqrt{2}\)
C. \(\sqrt{2}\)
D. \(2\)
E. \(2 \sqrt{2} \)
Given: \((5^{\sqrt{2}})^m=25\)
Apply the power of a power law to get: \((5^{m\sqrt{2}})=25\)
Rewrite \(25\) as \(5^2\) to get: \((5^{m\sqrt{2}})=5^2\)
So, it must be the case that: \(m\sqrt{2} = 2\)
Divide both sides of the equation by: \(\sqrt{2}\) to get: \(m = \frac{2}{\sqrt{2}}\)
This option does not appear among the answer choices, so we can create an equivalent fraction by multiplying numerator and denominator by \(\sqrt{2}\).
When we do so we get: \(m = \frac{2\sqrt{2}}{2}\)
Simplify to get: \(m = \sqrt{2}\)
Answer: C
Re: If (5^sqrtof2)^m=25
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04 Aug 2021, 06:56
04 Aug 2021, 06:56
1
5^(sqrt(2) * m) = 5 ^ 2
sqrt(2) * m = 2
m = sqrt(2)
ANS : C
sqrt(2) * m = 2
m = sqrt(2)
ANS : C
