Find the domain of the logarithmic function and then graph the function
\[
y=\ln (5 x+2)
\]
Find the domain of the function
(Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.)
Answer
Final Answer: The domain of the function is \(\boxed{(-2/5, \infty)}\)
Step 1 ：The domain of a logarithmic function is the set of all real numbers for which the argument of the logarithm is positive. In this case, we need to find the set of all x such that \(5x + 2 > 0\).
Step 2 ：Solving the inequality \(5x + 2 > 0\) gives \(x > -2/5\).
Step 3 ：So, the domain of the function is all x such that \(x > -2/5\). This is the set of all real numbers greater than -2/5.
Step 4 ：Final Answer: The domain of the function is \(\boxed{(-2/5, \infty)}\)
