Question 201985: 3*4^x+2*9^x=5*6^x
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! 3*4^x +2*9^x =5*6^x
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take log all terms
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log(3*4^x) + log(2*9^x) = log(5*6^x),,,,log(a*b) = loga +log b
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log3 + log4^x +log2 +log9^x = log5 + log6^x
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log4^x +log9^x - log6^x = log5 -log3-log2
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,,,,,,,,loga^b = b*loga,,,loga-logb=log(a/b)
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xlog4 +xlog9 -xlog6 = log(5/3/2)
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x{log4 +log9-log6 } = log(.833)
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x{log(4*9/6) } = -.07918
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xlog6 = -.07918
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x(.77815) = -.07918
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x= - .10175
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check,,3*4^(-.102) +2*9^(-.102) = 5*6^(-.102)
4.2046 = 4.1666,,,approx 1% off,,,,ok
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