Final answer:
To find the domain of definition for the function log₇(0.2x + 1), set the inside of the logarithm greater than zero, resulting in x > -5, and express the domain as (-5, ∞).
Step-by-step explanation:
The student is asking how to find the domain of definition for the logarithmic function log₇(0.2x + 1). In order for a logarithmic function to be defined, the argument (0.2x + 1 in this case) must be positive. This implies that 0.2x + 1 > 0. Solving for x gives us x > -5. Therefore, the domain of definition for the function is x > -5, which can also be written in interval notation as (-5, ∞).