Final answer:
The domain of the function y=ln(8x+5) is all real numbers greater than -5/8.
Step-by-step explanation:
The domain of a function is the set of all the possible input values, or x-values, for which the function is defined. In this case, the function is y = ln(8x + 5), where ln represents the natural logarithm. The natural logarithm is defined for all positive input values. Therefore, the domain of the function is the set of all x-values that make 8x + 5 positive.
To find the domain, we need to solve the inequality 8x + 5 > 0.
- Subtract 5 from both sides: 8x > -5.
- Divide both sides by 8: x > -5/8.
The domain of the function is all real numbers greater than -5/8.