Final answer:
To evaluate logᵦ(x³/y), we can use the properties of logarithms to simplify the expression and find the answer.
Step-by-step explanation:
To evaluate logᵦ(x³/y), we can use the properties of logarithms. According to the property of the difference of logarithms, logᵦ(x/y) = logᵦ(x) - logᵦ(y). Since we are evaluating logᵦ(x³/y), we can apply this property twice. First, we have logᵦ(x³/y) = logᵦ(x³) - logᵦ(y). And then, applying the property again, we get logᵦ(x³) - logᵦ(y) = 3 * logᵦ(x) - logᵦ(y).
Substituting the given values, we have 3 * logᵦ(x) - logᵦ(y) = 3 * 2.3219 - 2.8074. Evaluating the expression gives us the final answer for logᵦ(x³/y).