For b 0 with b not equals to 1 what are the domain and range

For b 0 with b not equals to 1, what are the domain and range of f(x) = log_bx and why? Choose the correct domain below. D=(0, ), because the range of its inverse function g(x)=b^x

Solution

Taking the initial function, where f(X) = log(b) (X), it\'s inverse function will be:

Y = b^(X). Now we need to take in main if we made a change of basis of the original function, for ex: basis 10, this will be defined as: log(X) / log (b), where b must be >0. So the domain is (0, infinity).

Then, the correct option is A.