Final answer:
The domain of the function is all positive real numbers and the range is all positive real numbers.
Step-by-step explanation:
The domain of the function y = log5(6 * 6x) is determined by the restrictions on the input values. In this case, the logarithm function is only defined for positive values, so the expression inside the logarithm must be greater than zero:
6 * 6x > 0
We can solve this inequality by dividing both sides by 6:
6x > 0
x > 0
Therefore, the domain of the function is all positive real numbers. The range of the function is determined by the possible output values. Since the base of the logarithm is 5, the function can take any positive real number as its output. Hence, the range of the function is also all positive real numbers.