Question 1059970
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
:
-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
:
ln(8x^3) = 18
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Cancel logarithms by taking exp of both sides, note that ln is natural logarithm
:
8x^3 = e^18
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Divide both sides by 8
:
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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