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)?
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
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