Primarygun Posted July 30, 2004 Share Posted July 30, 2004 [MATH] log(x+y)/logx = log(x+y)/logy[/MATH] Can anybody show a calculation? I think that's a trick. Link to comment Share on other sites More sharing options...
Dave Posted July 30, 2004 Share Posted July 30, 2004 Sorry, what do you actually want to do with that equation? Link to comment Share on other sites More sharing options...
Primarygun Posted July 30, 2004 Author Share Posted July 30, 2004 solve for x in terms of y Link to comment Share on other sites More sharing options...
Dave Posted July 30, 2004 Share Posted July 30, 2004 Well, that looks pretty trivial from the face of it, but there are some technicalities. I don't know whether that's a typo, but you have the same numerator on both sides, so just cancel that out (unless x+y=1 in which case you're screwed) and then anti-log both sides. Link to comment Share on other sites More sharing options...
Freeman Posted July 30, 2004 Share Posted July 30, 2004 I got log y is positive or negative x.... Link to comment Share on other sites More sharing options...
Dave Posted July 30, 2004 Share Posted July 30, 2004 y can't be negative x otherwise the equation wouldn't hold (log(0) not defined). Link to comment Share on other sites More sharing options...
Freeman Posted July 30, 2004 Share Posted July 30, 2004 Touché! Link to comment Share on other sites More sharing options...
Dave Posted July 30, 2004 Share Posted July 30, 2004 Cheers I got the solution y=x also. I could swear that the question has a typo in it somewhere, that just seems too simple. Link to comment Share on other sites More sharing options...
Primarygun Posted July 31, 2004 Author Share Posted July 31, 2004 Well, that looks pretty trivial from the face of it, but there are some technicalities. I don't know whether that's a typo, but you have the same numerator on both sides, so just cancel that out (unless x+y=1 in which case you're screwed) and then anti-log both sides. x+y=1 x=y Ya there are two answers. But what makes you know that x+y=1 is also possible. Normally, don't us only cancel the log sign to find out x=y instead of minus the left side by the right side and then fing x+y=1? Link to comment Share on other sites More sharing options...
pulkit Posted July 31, 2004 Share Posted July 31, 2004 Look at the solution : [MATH]\frac{\log(x+y)}{\log(x)} = \frac{\log(x+y)}{\log(y)}[/MATH] [MATH]\log(x+y) \times (\frac{1}{\log(x)} - \frac{1}{\log(y)}) = 0[/MATH] [MATH]\Rightarrow \log(x+y) = 0 \ldots or \ldots \frac{1}{\log(x)}=\frac{1}{\log(y)}[/MATH] [MATH]\Rightarrow x+y=1 \ldots or \ldots \log(x)=\log(y)[/MATH] [MATH]\Rightarrow x+y=1 \ldots or \ldots x=y [/MATH] Link to comment Share on other sites More sharing options...
Primarygun Posted July 31, 2004 Author Share Posted July 31, 2004 yes I know it. But why do you use this method? Normally, don't we use the cross-method calculation only? If I don't say there has a trick or there are two possible answers, how many answers do you desire to get? Link to comment Share on other sites More sharing options...
pulkit Posted July 31, 2004 Share Posted July 31, 2004 When you cancel out a term from both sides, you always assume that this term is non-zero. Hence you must consider the case of this term being zero seperately. In the particular question this term is [MATH]\log(x+y)[/MATH] and [MATH]x+y=1[/MATH] comes out of the case when it is zero. Link to comment Share on other sites More sharing options...
Dave Posted July 31, 2004 Share Posted July 31, 2004 sigh. I suck Link to comment Share on other sites More sharing options...
Primarygun Posted August 2, 2004 Author Share Posted August 2, 2004 When you cancel out a term from both sides, you always assume that this term is non-zero. Hence you must consider the case of this term being zero seperately. In the particular question this term is [MATH]\log(x+y)[/MATH] and [MATH]x+y=1[/MATH'] comes out of the case when it is zero. Thanks. Is there any other cases for other regions of mathematics? Link to comment Share on other sites More sharing options...
pulkit Posted August 2, 2004 Share Posted August 2, 2004 Is there any other cases for other regions of mathematics? What do you mean ? Link to comment Share on other sites More sharing options...
Primarygun Posted August 3, 2004 Author Share Posted August 3, 2004 such as normal algebra. Link to comment Share on other sites More sharing options...
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