Question

Tho domain of a logarithmic function y=logbx , where b is a positive real number not equal to one, is _____.

a. all numbers greater than one
b. all real numbers
c. all positive real numbers
d. all negative real numbers

Answer 1

The domain of the logarithmic function y=logbx is all positive real numbers because a positive base raised to any power cannot result in a negative number or zero.

Step-by-step explanation:

The domain of a logarithmic function y=logbx, where b is a positive real number not equal to one, is all positive real numbers. This is because a logarithm represents the exponent to which the base ‘b’ must be raised to produce ‘x’. Since raising a positive number to any power will never result in a negative number or zero, the input value ‘x’ for a logarithmic function must be greater than zero. Therefore, the correct answer is an option (c) all positive real numbers.