Question 135168: okay i have two problems
2^(2/3x+1)-3x2^(1/3x)-20=0
also,
2^2x-1 -3x2^x-1 +1=0
help, please.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 2^[(2/3)x+1)-3[2^(1/3x)]-20=0
2[2^(x/3)^2] - 3[2(x/3)] - 20 = 0
Let 2^(x/3) = w
2w^2 -3w -20 = 0
(w-4)(2w-5) = 0
w = 4 or w = 5/2
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Therefore:
2^(x/3) = 4 or 2^(x/3) = 5/2
2^(x/3) = 2^2 or (x/3)log2 = log(5/2)
x/3 = 2 or (x/3) = [log(5/2)]/[log2]
x = 6 or x = 3[0.9193] = 2.7580
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also,
2^2x-1 -3x2^x-1 +1=0
(1/2)(2^x)^2 - (3/2)(2^x) +1 = 0
Let 2^x = w
(1/2)w^2 -(3/2)w + 1 = 0
w^2 - 3w + 2 = 0
(w-1)(w-2) = 0
w = 1 or w = 2
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2^x = 1 or 2^x = 2
x = 0 or x = 1
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Cheers,
Stan H.
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