Logarithmic Properties and Evaluations

The video tutorial explains how to evaluate given logarithms by expanding them using properties such as the quotient, product, and power properties. It provides two examples where the logarithms are expanded and evaluated using substitution based on given values. The first example involves expanding a quotient of logs, while the second example focuses on expanding a product of logs. The tutorial emphasizes careful application of logarithmic properties and substitution to arrive at the final evaluated expressions.

What is the first step in evaluating the given logarithms?

• Ignoring the given values

• Using the power property immediately

• Expanding the logarithms as much as possible

• Performing substitution directly

In the first example, how is a quotient of logs expressed?

• As a power of two logs

• As a difference of two logs

• As a product of two logs

• As a sum of two logs

What property is used to expand a product of logs?

• Power property

• Product property

• Quotient property

• Substitution property

How do you handle the subtraction of expanded logs?

• Subtract the expansion of the logs

• Add the logs

• Multiply the logs

• Divide the logs

What is the result of the first example after substitution?

• -21

• 0

• 21

• -42

In the second example, how is the exponent divided?

• By the base

• By the index

• By the coefficient

• By the logarithm

What is the result of applying the product property in the second example?

• A quotient of three logs

• A product of three logs

• A difference of three logs

• A sum of three logs

How are exponents handled in logarithmic expressions?

• They are ignored

• They are added to the base

• They become coefficients

• They are subtracted from the base

What is the final result of the second example after substitution?

• 28/3

• 56/3

• 42/3

• 14/3

What is the main purpose of expanding logarithms in these examples?

• To make them more complex

• To simplify and evaluate them

• To change their base

• To ignore given values