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Natural Logarithmic Equation ln (x-1) - ln x = ln 49

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rosey-girl | Student, Grade 12 | Valedictorian

Posted April 23, 2013 at 5:24 AM via web

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Natural Logarithmic Equation

ln (x-1) - ln x = ln 49

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 23, 2013 at 5:29 AM (Answer #1)

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The equation ln (x-1) - ln x = ln 49 has to be solved.

Use the property ln x - ln y = ln(x/y)

ln (x-1) - ln x = ln 49

=> ln((x - 1)/x) = ln 49

(x - 1)/x = 49

=> x - 1 = 49x

=> 48x = -1

=> x = -1/48

But the logarithm of a negative number does not exist.

The equation has no solution.

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