Logarithmic Properties and Expansion

The video tutorial explains how to expand a logarithmic expression using the properties of logarithms. It begins with an introduction to the expression and then applies the quotient property to separate the logarithm of a division into a difference of logarithms. Next, the product property is used to further expand the logarithms of products into sums. The tutorial concludes with a final expansion and a summary of the steps involved.

What is the initial expression given for expansion using logarithmic properties?

• log base 3 of (2x * x - 3) / (2x - 1 * x + 4)

• log base 3 of (2x - 3) / (2x + 1)

• log base 3 of (2x * (x - 3)) / ((2x - 1) * (x + 4))

• log base 3 of (2x + x - 3) / (2x - 1 + x + 4)

Which property of logarithms is used to separate the log of a quotient into two logs?

• Quotient Property

• Change of Base Property

• Power Property

• Product Property

After applying the quotient property, what is the next step in expanding the expression?

• Apply the power property

• Simplify the expression

• Apply the product property

• Combine like terms

How many factors are in the numerator of the expression after applying the quotient property?

• One

• Three

• Two

• Four

What is the result of expanding log base 3 of (2x * (x - 3)) using the product property?

• log base 3 of (2 + x - 3)

• log base 3 of 2x + log base 3 of (x - 3)

• log base 3 of 2 + log base 3 of x + log base 3 of (x - 3)

• log base 3 of 2 + log base 3 of x - 3

What must be done when expanding a logarithm that involves subtraction?

• Add the expansions

• Multiply the expansions

• Subtract the expansions

• Divide the expansions

What is the expanded form of log base 3 of ((2x - 1) * (x + 4))?

• log base 3 of (2x - 1) / log base 3 of (x + 4)

• log base 3 of (2x - 1) * log base 3 of (x + 4)

• log base 3 of (2x - 1) - log base 3 of (x + 4)

• log base 3 of (2x - 1) + log base 3 of (x + 4)

What is the final step in the expansion process?

• Factor the expression

• Add all the logs together

• Distribute the negative sign

• Combine like terms

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

• log base 3 of 2 + log base 3 of x + log base 3 of (x - 3) + log base 3 of (2x - 1) + log base 3 of (x + 4)

• log base 3 of 2 - log base 3 of x + log base 3 of (x - 3) + log base 3 of (2x - 1) - log base 3 of (x + 4)

• log base 3 of 2 + log base 3 of x - log base 3 of (x - 3) + log base 3 of (2x - 1) + log base 3 of (x + 4)

• log base 3 of 2 + log base 3 of x + log base 3 of (x - 3) - log base 3 of (2x - 1) - log base 3 of (x + 4)

Why is it important to distribute the negative sign in the final step?

• To correctly apply the product property

• To simplify the expression

• To accurately reflect the subtraction in the original expression

• To ensure the correct order of operations