Question 1059970: good morning
would you help me find the logarithmic equation
6+ln(8x)=24-2 ln(x) Found 2 solutions by stanbon, rothauserc:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! 6+ln(8x)=24-2 ln(x)
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ln(8x)+ln(x^2) = 24-6
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ln[x^2*8x] = 18
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8x^3 = e^18
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x^3 = e^18/8
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x = (e^6)/2
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x = 210.71
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Cheers,
Stan H.
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You can put this solution on YOUR website! Solve for x over the real numbers
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6 + ln(8x) = 24 - 2ln(x)
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Subtract 24 - 2 ln(x) from both sides
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-18 + 2ln(x) + ln(8x) = 0
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-18 + 2ln(x) + ln(8x) = -18 + ln(8x) + ln(x^2) = ln(8x^3) - 18
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Note that c(ln(x)) = ln(x^c) where c is a constant, then we use the product rule of logarithms
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ln(8x^3) - 18 = 0
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Add 18 to both sides
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ln(8x^3) = 18
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Cancel logarithms by taking exp of both sides, note that ln is natural logarithm
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8x^3 = e^18
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Divide both sides by 8
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x^3 = e^18/8
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Take cube roots of both sides
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x = e^6/2
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Note that e is approximately 2.71828
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x = (2.71828)^6 / 2 is approximately 201.7144
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