what are the domain and range of (f(x)=log x - 5)?\no domain: (x > 0); range: all real numbers\no domain: (x…

what are the domain and range of (f(x)=log x - 5)?\no domain: (x > 0); range: all real numbers\no domain: (x < 0); range: all real numbers\no domain: (x > 5); range: (y > 5)\no domain: (x > 5); range: (y > - 5)

what are the domain and range of (f(x)=log x - 5)?\no domain: (x > 0); range: all real numbers\no domain: (x < 0); range: all real numbers\no domain: (x > 5); range: (y > 5)\no domain: (x > 5); range: (y > - 5)

Answer

Explanation:

Step1: Recall domain of logarithmic function

The argument of the logarithm $\log x$ must be positive. So for $y = \log x-5$, we have $x>0$.

Step2: Analyze range of logarithmic function

The basic logarithmic function $y = \log x$ has a range of all real numbers. Subtracting 5 from $\log x$ does not change the range. So the range of $y=\log x - 5$ is all real numbers.

Answer:

domain: $x > 0$; range: all real numbers