Algebra

ronnie's Avatar
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19 Apr 2012 23:33:34 IST
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logarithm fallacy???
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

log(1+2+3)=log1+log2+log3..possible...does it happen lyk ds???



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Blazing goIITian

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19 Apr 2012 23:43:26 IST
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Yes it happenes in many cases so no wonder
ronnie's Avatar

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20 Apr 2012 00:01:22 IST
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specify cases......(if u feel it happens)
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20 Apr 2012 00:29:37 IST
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If A, B, C are the angles of ACUTE angled triangle. 

Then,

 

tanA.tanB.tanC = tanA + tanB + tanC

 

log(tanA + tanB + tanC) = log(tanA) + log(tanB)  + log(tanC) 

 

Bucaneer:10504

sudhindra shenoy's Avatar

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20 Apr 2012 06:54:49 IST
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yes, of course

Bipin Dubey's Avatar

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20 Apr 2012 13:02:19 IST
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log(a+b+c) = loga + logb + logc is possible when a+b+c=abc

Examples : (2 , 4 , 6/7) ; (3 , 4 , 7/11)

Generalization : (x , y , (x+y)/(xy-1))....for above expression to be valid you can pick any x & y keeping in mind all numbers in triplet are positive.


Hot goIITian

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20 Apr 2012 15:56:04 IST
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I agree with Bipin Dubey....Just abc=a+b+c, is req condition generally..( But Log should not become undefined for value of log a,b,c, or a+b+c):)
ronnie's Avatar

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21 Apr 2012 17:36:00 IST
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i got this result from dis log(1+3x+2x^2)=log((2x+1)(x+1))
GOPAKUMAR's Avatar

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22 Apr 2012 07:55:18 IST
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@ronnie what u hav written is more or less like log(a) = log(a) it is nothing to do with the ques the ques u have asked is about

if a+b+c = abc then log(a+b+c)=log(abc)

provided the satisfy the domain criteria of the function log(x)....................

ronnie's Avatar

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22 Apr 2012 13:37:38 IST
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are pagle,put d value of x=1 and log1=0..u wl undrstnd.....
GOPAKUMAR's Avatar

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22 Apr 2012 17:57:29 IST
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listen if u put x=1 in log(1+3x+2x^2)=log((2x+1)(x+1))

u get log(6)=log(6)

got it ..........happy




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