Question #a2865
1 Answer
The important property we need to solve this problem follows from the rule of addition for exponents:
By definition of logarithm,
If
Then above rule of addition of exponents can be written as
This is a theorem about addition of logarithms.
Therefore, based on the rule of addition of exponents and the definition of logarithm,
By definition of logarithm mentioned above for
Hence,
which can be directly derived from the theorem about addition of logarithms as
Also notice that, since
Therefore, our entire expression can be represented as
Using the theorem about addition of logarithms, this is equal to