What is the domain of the logarithmic function 𝑦=log10(𝑥)? Give your answer using inteval notation; e.g. oc(2,3) for (2,3].

Break Down the Problem

1. Identify the properties of the logarithmic function.
2. Determine the values of $x$ for which $y = \log_{10}(x)$ is defined.

Relevant Concepts

1. The logarithmic function $\log_{10}(x)$ is defined for $x > 0$.
2. The domain of a function is the set of all possible input values (x-values) that does not lead to undefined results (like negative values or zero in the case of logarithms).

Analysis and Detail

1. Since $\log_{10}(x)$ is only defined for positive values of $x$, we can express this restriction mathematically: $x > 0$
2. This means that $x$ can take any value greater than zero, but not equal to zero or any negative value.

Verify and Summarize

The logarithmic function $y = \log_{10}(x)$ has no issues at values of $x > 0$, confirming that the domain consists solely of positive real numbers.

Final Answer

The domain of the function $y=\log_{10}(x)$ in interval notation is $(0, \infty)$.