Question

For log_b(x), what are the domain and range?

a) Domain: x > 0, Range: R
b) Domain: x > 0, Range: R+
c) Domain: x ≠ 1, Range: R
d) Domain: x ≠ 1, Range: R+

Answer 1

The domain of log_b(x) is x > 0 and the range depends on the value of b.

Step-by-step explanation:

The domain of the logarithm function logb(x) is given by x > 0, as the logarithm of a negative number or zero is undefined. This means that the input value x must be greater than zero. The range of the logarithm function depends on the base b. If b > 1, the range is R+ (positive real numbers). If 0 < b < 1, the range is R (all real numbers).