Final answer:
To express log3(6/5) in terms of log3(2) and log3(5), we use the logarithmic properties of quotients and products. The correct expression is log3(2) - log3(5), which corresponds to option B.
Step-by-step explanation:
We want to express log3(6/5) in terms of log3(2) and log3(5). Using the property of logarithms that states the logarithm of a quotient is the difference of the logarithms, we get:
log3(6/5) = log3(6) - log3(5)
Since 6 can be expressed as 2 × 3, and we have the property that the logarithm of a product is the sum of the logarithms, we can write:
log3(6) = log3(2 × 3) = log3(2) + log3(3)
Because log3(3) is equal to 1, the equation simplifies to:
log3(6) = log3(2) + 1
Substituting back into the original expression, we get:
log3(6/5) = (log3(2) + 1) - log3(5) = log3(2) - log3(5)
Thus, the correct answer is B. log32 - log35.