Which property justifies simplifying the expression logb^(b^x+y) to x+y in the proof for the product property of logarithms? A) b^x¬¨‚àëb^y = b^(x+y) B) Substitution C) logb^(b^c) = c D) Commutative property

Mathematics Questions

Which property justifies simplifying the expression logb^(b^x+y) to x+y in the proof for the product property of logarithms? A) b^x¬¨‚àëb^y = b^(x+y) B) Substitution C) logb^(b^c) = c D) Commutative property

Short Answer

To simplify a logarithmic expression, first familiarize yourself with the properties of logarithmic functions. Then, clearly write down the expression, and apply the evaluation property to simplify it effectively, leading to the correct solution.

Step-by-Step Solution

Step 1: Identify Logarithmic Properties

Begin by understanding the properties of logarithmic functions, as these will be essential in simplifying the expression. Familiarize yourself with how logarithms work, including rules like the product, quotient, and power rules. This foundational knowledge will guide you in determining the correct transformations for the expression.

Step 2: Write the Logarithmic Expression

Clearly write down the logarithmic expression you are working with, which is rm log(b)^{b^{x+y}}. Presenting the expression in this format allows you to see what needs simplification and enables you to apply the properties more effectively. Make sure to organize it neatly for clarity.

Step 3: Apply the Evaluation Property

Utilize the property rm log(b)^{b^{c}}=c to evaluate the expression. By recognizing that the given logarithmic expression can be simplified using this property, you can arrive at the solution efficiently. Consequently, you will find that the correct option stands as C).

Which property justifies simplifying the expression logb^(b^x+y) to x+y in …