Logarithmic Properties and Factoring

The video tutorial explains how to expand a logarithmic expression using properties of logarithms. It begins by introducing the concept of expanding logarithms and identifying the expression to be expanded. The tutorial then demonstrates how to factor and simplify the expression by identifying common factors in the numerator and denominator. After simplifying, the video shows how to expand the logarithm using the quotient and product properties, resulting in a sum and difference of logarithms. The tutorial concludes with additional notes on the expansion process and emphasizes the importance of simplifying before expanding.

What is the base of the logarithm if it is not specified?

• Base 5

• Base 2

• Base 10

• Base e

What is the greatest common factor of the numerator 3x^2 + 9x?

• 3x

• 9

• x

• 3

After factoring, what does the expression 2x + 6 become?

• x + 6

• 2x + 3

• 2(x + 3)

• x(2 + 6)

What is the purpose of factoring the expression before expanding the logarithm?

• To change the base of the logarithm

• To simplify the expression

• To make the expression more complex

• To eliminate the logarithm

What happens to the expression when x + 3 is canceled out from the numerator and denominator?

• It becomes one

• It becomes log(2x/3)

• It becomes log(3x/2)

• It becomes zero

How can the log of a quotient be expressed?

• As a difference of logs

• As a product of logs

• As a division of logs

• As a sum of logs

What is the expanded form of log(3x) using the product property?

• log(3x) + log(2)

• log(3x) - log(2)

• log(3) + log(x)

• log(3) - log(x)

What is the final expanded form of the given logarithmic expression?

• log(3) + log(x) - log(2)

• log(3) + log(x) + log(2)

• log(3) - log(x) + log(2)

• log(3x) - log(2)

Which property of logarithms allows us to express log(3x) as log(3) + log(x)?

• Power property

• Change of base property

• Product property

• Quotient property

What would happen if the logarithm was expanded without simplifying first?

• The result would be incorrect

• The result would be the same

• The result would be log(3x/2)

• The result would be log(2x/3)