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How to solve for x equation ln(3x-24)=ln(1-2x)?
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First, you'll have to impose constraints of existence of the logarithms:
3x-24 > 0
3x > 24
x > 8
1 - 2x > 0
-2x > -1 <=> 2x < 1 => x < 1/2
Since the logarithms have common bases, we'll equate the numbers, using the one to one property of logarithms:
3x - 24 = 1 - 2x
3x + 2x = 24 + 1
5x = 25
x = 5
Since the value of x does not satisfy both conditions of existence of logarithms, therefore the equation has no valid solution.
Posted by giorgiana1976 on August 2, 2011 at 8:27 PM (Answer #1)
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