Final answer:
To complete the equation log3(32)=log3(34)+_, the missing expression is log3(3). This is because log3(32) can be expressed as log3(3 * 4), which simplifies to log3(3) + log3(4).
Step-by-step explanation:
To solve the equation log3(32)=log3(34)+_, we need to find an expression that will make the equation true. According to the properties of logarithms, specifically the property that the logarithm of a product is equal to the sum of the logarithms (loga(bc) = loga(b) + loga(c)), we can infer that log3(32) is equivalent to log3(3 * 4) which is the same as log3(3) + log3(4).
Given the equation log3(32) = log3(34) + _, we can substitute and see that log3(4) is already present on both sides. Since log3(32) = log3(3 * 4) can be written as log3(3) + log3(4), the missing part is simply log3(3) or option (a) log3(3).