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Joined:	19 Apr 2012
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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)?

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mihir sethi

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3 May 2012 22:56:05 IST

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all real no. except 3

Bipin Dubey

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Joined: 23 Jan 2007

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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

Shantanu Gontia

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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}

mihir sethi

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3 May 2012 23:55:32 IST

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yes

mihir sethi

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3 May 2012 23:56:28 IST

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in both cases we will write R-{3}

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