Final answer:
The sum log(3)6 + log(3)13.5 can be expressed as a single logarithm log(3)(6 \times 13.5), which further simplifies to log(3)(81). Since 3^4 equals 81, the value of the logarithm is 4.
Step-by-step explanation:
The expression log(3)6 + log(3)13.5 can be combined into a single logarithm using the property that the logarithm of a product is equal to the sum of the logarithms of the factors (the product rule for logarithms). Therefore, we can write:
log(3)6 + log(3)13.5 = log(3)(6 \times 13.5) = log(3)(81)
Knowing that 3^4 = 81, we can evaluate the single logarithm as follows:
log(3)(81) = 4
The final answer is 4, and this is because we have used the property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number (the power rule for logarithms).