Final answer:
The expression simplifies by using basic properties of logarithms and the expression given reduces to log of a term minus log of the same term, which is zero, so the entire expression simplifies to zero.
Step-by-step explanation:
In order to simplify the expression, we need to use some basic properties of logarithms. Firstly, the sum of two logs is the log of their product and the difference of two logs is the log of their quotient. So, we can rewrite the expression by applying these rules as follows: log(u³) + log(v²) - log[(u/v)³] - 5 log(v)
can be rewritten as log(u³v²) - log[(u/v)³v⁵]. Next, for the expressions under the logs, we can simplify them because when a term is raised to an exponent in a log, the term can be brought down as a coefficient: (u/v)³v⁵
= (u³/v³)v⁵ = u³v². This simplifies to log(u³v²) - log(u³v²). The difference of a log from itself is zero, so the entire expression simplifies to zero.
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