Final answer:
The domain of a logarithmic function is found by ensuring the argument of the log is positive. For a common logarithm with base 10, this means the domain is all real numbers greater than zero.
Step-by-step explanation:
How to Find the Domain of a Logarithmic Function
To find the domain of a logarithmic function, one must remember that the argument (the value inside the log function) must always be positive. Since logarithms represent the exponent to which a base (commonly 10 for the common logarithm) is raised to obtain the argument, the argument cannot be zero or negative. Let's go through the steps for identifying the domain of the function f(x) = log10(x).
- Recognize that logarithmic functions are the inverses of exponential functions.
- Identify the base of the logarithm; for common logarithms, it is 10.
- Set the argument greater than zero (x > 0) because the base raised to any real number will never result in a non-positive number.
- Solve the inequality x > 0. This will provide the set of all possible x values that make the function defined and real
Therefore, the domain of the function f(x) = log10(x) is all real numbers greater than zero.