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Updated on: 06 Jan 2016, 07:59
Originally posted by timothyhenman1 on 05 Jan 2016, 22:21.
Last edited by Bunuel on 06 Jan 2016, 07:59, edited 1 time in total.
Last edited by Bunuel on 06 Jan 2016, 07:59, edited 1 time in total.
Renamed the topic and edited the question.
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If x is a positive integer such that \(4*2^{(x+2.5)} =\sqrt{2}*0.5^{(-3x)}\). What is the value of \(x^3\)?
A) 2
B) 3
C) 5
D) 7
E) 8
A) 2
B) 3
C) 5
D) 7
E) 8
06 Jan 2016, 05:30
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timothyhenman1
If x is a positive integer such that 4*2^(x+2.5) = \(\sqrt{2}\)*0.5^(-3x)
What is the value of \(X^3\)?
A)2
B)3
C)5
D)7
E)8
What is the value of \(X^3\)?
A)2
B)3
C)5
D)7
E)8
This can be solved by bringing every term to the same base.
\(4*2^{x+2.5}\) = \(\sqrt{2}\)*\(0.5^{-3x}\)
\(2^2*2^{x+2.5}\) = \(2^{1/2}\)*\((1/2)^{-3x}\)
\(2^{x +4.5}\) =\(2^{1/2}\)*\((2)^{3x}\)
\(2^{x +4.5}\) =\(2^{3x + 0.5}\)
Equating the powers,
x + 4.5 = 3x + 0.5
2x = 4, x = 2
Hence, \(2^3\) = 8 Option E
General Discussion
06 Jan 2016, 11:36
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timothyhenman1
If x is a positive integer such that 4*2^(x+2.5) = \(\sqrt{2}\)*0.5^(-3x)
What is the value of \(X^3\)?
A)2
B)3
C)5
D)7
E)8
What is the value of \(X^3\)?
A)2
B)3
C)5
D)7
E)8
This can be solved by bringing every term to the same base.
\(4*2^{x+2.5}\) = \(\sqrt{2}\)*\(0.5^{-3x}\)
\(2^2*2^{x+2.5}\) = \(2^{1/2}\)*\((1/2)^{-3x}\)
\(2^{x +4.5}\) =\(2^{1/2}\)*\((2)^{3x}\)
\(2^{x +4.5}\) =\(2^{3x + 0.5}\)
Equating the powers,
x + 4.5 = 3x + 0.5
2x = 4, x = 2
Hence, \(2^3\) = 8 Option E
Ugh! I feel so stupid, my first instinct was to change the base of the 4 to 2^2 but when it came to the second side of the eqn i my brain completely forgot that i can change root2 to 2^1/2 and .5^-3x completely intimidated me to the point where i ended up just guessing on the test.
thanks for your help in explaining this, it really helps. I will now go back and review those pesky exponent rules and tricks.
