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Show that functions f and g defined by f(x)=2 log x and g(x)=log x^2 are not equal even though log x^2 =2 log x.

Answer»

Solution :`F(X)=2 "log"x`
`g(x)="log" x^2`
`"DOM" f(x) = (0,oo)`
`"Dom" g(x) =R-{0} `
`"As Dom" f(x) != Dom g(x) "we have" f(x) !=g(x), "though log" x^2 =2"log"x`


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