179k views
5 votes
Complete the equation with an expression that makes it true. log332=log34+_

a) log3(3)
b) log3(4)
c) log3(12)
d) log3(9)

User Sunny Moon
by
8.2k points

1 Answer

4 votes

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).

User Jacob Mattison
by
8.0k points