Short Answer 
Proofs are crucial in mathematics for validating statements and are built on definitions, logical reasoning, and established theorems. In this context, the key logarithmic expressions lead to the deduction of the missing expression, logb((bxy)), which clarifies logarithmic relationships.
Step 1: Understand the Role of Proofs
Proofs are essential in mathematics as they are used to establish the validity of a given statement. They help in confirming or disproving mathematical assertions, providing a foundation for further exploration. The key components of a proof include definitions, logical reasoning, and established theorems.
Step 2: Identify the Key Expressions
In the given context, we first need to consider the specific logarithmic expressions related to exponents. The expressions to focus on include:
- logb(My)
- logb((bx)y)
These expressions will lead us to the core concept behind the missing expression in the proof.
Step 3: Derive the Missing Expression
Utilizing the properties of exponents, we can simplify the identified expressions to arrive at the missing element. This expression is:
- logb((bxy))
This confirms that the missing expression in this proof is indeed logb((bxy)), which completes the argument and solidifies the understanding of logarithmic relationships.