Final answer:
The question addresses properties of logarithmic functions, explaining how they increase and how to manipulate expressions using logarithm laws.
Step-by-step explanation:
The student is asking about properties of logarithmic functions, specifically about how functions of the form f(x) = log3 x and g(x) = 4 log3 (x + 1) behave. The questions provided relate to logarithms' properties that tell us, for instance, as x increases, the log(x) also increases at a decreasing rate. Another property is that the logarithm of a number raised to an exponent is the product of that exponent and the log of the number, as shown in g(x), where the logarithm is multiplied by 4. Additionally, the logarithm of a product of two numbers is the sum of the logs of the numbers, and conversely, the logarithm of a quotient is the difference of the logs. These properties are essential for simplifying and understanding the behavior of logarithmic equations in algebra and calculus.