Final answer:
The logarithmic expression log₃(36x + 27y) cannot be expanded using standard logarithmic properties because it involves a sum (36x + 27y) and not a product or an exponent, which are required for the product and exponent rules.
Step-by-step explanation:
To expand the logarithmic expression log₃(36x + 27y), we need to apply logarithmic properties. However, it's important to note that logarithmic properties such as the product rule (log a*b = log a + log b) and the exponent rule (log a^n = n*log a) can only be applied when the log arguments are products or powers, not sums. In this expression, 36x and 27y are added together, not multiplied, so these properties cannot be directly applied.
If 36x and 27y were factors instead of a sum, then we could expand the logarithm by applying the product rule, writing it as log₃(36) + log₃(x) and log₃(27) + log₃(y), and subsequently applying the exponent rule if applicable. However, since this is not the case, the expression log₃(36x + 27y) cannot be further expanded using standard logarithmic properties.