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Question

If f(x)=log(x2)+log(x3) and ϕ(x)=log(x2)(x3).
Are both functions equal?

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Solution

For f(x) to be defined, x2>0 and x3>0
So domain of f(x) is (3,)
And for ϕ(x) to be defined (x2)(x3)>0
x(,2)(3,)= domain of ϕ(x)
But we know that two function are same, if their range ,domain and values at each x is equal
Hence here f and ϕ are not equal

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