Problem

Find the domain of the logarithmic function and then graph the function
y=ln⁡(5x+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

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Answer

Final Answer: The domain of the function is (−2/5,∞)

Steps

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 (−2/5,∞)

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