Question 757375: (1) If(2/3)^m=72/243, find m. (2) find the coefficient of x^8 in (x^2+2y/x)^10
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! (1) If(2/3)^m=72/243, find m.
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Since the variable is in the exponent, take the log of both sides.
m*log(2/3) = log(72/243)
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m = [log(72/243)]/[log(2/3)] = 3
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(2) find the coefficient of x^8 in (x^2+2y/x)^10
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Form of each term of the expansion:
(x^2)^(10-a)(2y/x)^a = x^(20-2a)/x^a = x^(20-3a)
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Solve for "a"
20-3a = 8
-3a = -12
a = 4
10-a = 6
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The term with a = 4 and 10-a = 6
10C6 (x^2)^6*(2y/x)^4 = 210[x^12 * 16y^4/x^4]
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= 210*16 x^8*y^4
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= 3360 x^8y^4
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Cheers,
Stan H.
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