e and ln

**pop_91** · November 14th 2009, 02:08 AM

I have half done this question and icant seem to finish it im completely suck.. so any help is appreciated

Find the exact values of x for which...

(e^x)/(((e^x)-2)^2) = 1

**e^(i*pi)** · November 14th 2009, 02:38 AM

Originally Posted by pop_91

I have half done this question and icant seem to finish it im completely suck.. so any help is appreciated

Find the exact values of x for which...

(e^x)/(((e^x)-2)^2) = 1

It's refreshing to see a unambiguously written equation

$\frac{e^x}{(e^x -2)^2} = 1$

$e^x = (e^x-2)^2$

Expand the right hand size as per the binomial theorem/normal quadratic

$e^x = (e^x)^2 - 4e^x + 4$

$(e^x)^2 - 5e^x +4 = 0$

This is a quadratic in $e^x$ and so the quadratic equation can be used - however this one factorises

$(e^x-4)(e^x-1) = 0$

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e and ln