Let
In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:
So, the base case is ok. Now, we need to assume and prove
.
states that
Since we're assuming , we can substitute the sum of the first n terms with their expression:
Which terminates the proof, since we showed that
as required
The property used to rewrite the given expression is product property.
Answer: Option A
<u>Step-by-step explanation:</u>
Given equation:
The sum of the two logarithms of two quantities (on the same basis) corresponds to the logarithm of their product on the same basis. The product log is equal to the log’s sum of the factors.
There are several rules that you can use to solve logarithmic equations. One of these guidelines is the logarithmic products rule that you can use to differentiate complex protocols in different ways. Different values that can be valuable are the quota principle and the logarithm rule. The logarithmic products rule is essential and is regularly used in analysis to control logs and simplify baseline conditions.