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Algebra

Cool goIITian

 Joined: 19 Apr 2012 Post: 53
3 May 2012 22:12:35 IST
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Logarithm Doubt
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

If  say i am given f(x) = 2 log (x-3)  and i am supposed to find out the domain for the f(x). Do i need to worry about the fact that logarithm needs to have values > 0 . now 2 log(x-3) = log(x-3)^2 which belongs to positive real numbers or 0 for all real values of x. so what would be the domain of f(x)?

Hot goIITian

Joined: 8 Oct 2011
Posts: 120
3 May 2012 22:56:05 IST
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all real no. except 3

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Joined: 23 Jan 2007
Posts: 7958
3 May 2012 23:23:37 IST
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2log(x-3) and log(x-3)^2 are different when we talk of domain (their values will be same under their respective domains)

2log(x-3) has domain x-3>0  =>  x>3........while log(x-3)^2 has domain x not equal to 3

Cool goIITian

Joined: 19 Apr 2012
Posts: 53
3 May 2012 23:32:57 IST
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so if in a question i am specified explicitly , 2log(x-3) the domain will be x>3 and if i'm specified log(x-3)^2, i write the domain R-{3}

Hot goIITian

Joined: 8 Oct 2011
Posts: 120
3 May 2012 23:55:32 IST
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yes

Hot goIITian

Joined: 8 Oct 2011
Posts: 120
3 May 2012 23:56:28 IST
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in both cases we will write R-{3}

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