Logarithm EquationDate: 01/22/2002 at 14:28:30 From: Timmy Subject: A strange logarithm equation This equation, which I've tried to solve, has turned out to be impossible for my skills! 2x^2-1 = ln(2x^2) If there is some way to solve this I'd be really grateful to know. Date: 01/22/2002 at 14:40:07 From: Doctor Paul Subject: Re: A strange logarithm equation After fiddling with this for a minute, it occured to me that this was a pretty hard problem unless it was designed to be solved. And as it turns out, this problem is designed to be solved. Here's how to do it: I figured I had nothing to lose if I just decided to see where the left-hand side and the right-hand side had roots. If they both have roots at the same place, then I've found a solution to the problem. 2x^2 - 1 = 0 x = +- 1/sqrt(2) = +- sqrt(2)/2 ln(2x^2) = 0 is true when 2x^2 = 1 and that implies x = +- 1/sqrt(2) = +- sqrt(2)/2 So it turns out that the two solutions to this problem are x = +- sqrt(2)/2. Sometimes it helps to know that these sorts of problems will have solutions. So finding them might involve unusual techniques. But if you know there is a solution and it's going to be a reasonable solution, then finding it usually isn't too difficult. I hope this helps. Please write back if you'd like to talk about this more. - Doctor Paul, The Math Forum http://mathforum.org/dr.math/ |
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