Expanding and Condensing Logarithms Mastery

The video tutorial covers the properties of logarithms, focusing on condensing and expanding them. It explains the product, quotient, and power properties with examples. The product property involves expanding logarithms with multiplication into addition, while the quotient property uses division to expand into subtraction. The power property allows exponents to be moved in front of the logarithm. The tutorial includes examples of expanding and condensing logarithmic expressions, emphasizing the importance of having a single logarithm in the final answer.

What does the product property of logarithms allow us to do?

• Condense two logarithms into a single logarithm using multiplication

• Expand a single logarithm into the sum of two logarithms

• Subtract one logarithm from another

• Divide two logarithms

How can we condense log base 4 of Z plus log base 4 of W?

• log base 4 of Z/W

• log base 4 of ZW

• log base 4 of Z + W

• log base 4 of Z - W

What property is used to expand log base 7 of X divided by 3?

• Quotient property

• Product property

• Base property

• Power property

How do we condense a logarithm with a subtraction inside?

• By multiplying the components

• By dividing the components

• By adding the components

• By subtracting the components

What does the power property allow us to do with the exponent in a logarithm?

• Divide the logarithm by it

• Move it to the front of the logarithm

• Multiply it by the base

• Ignore it

In the expression log base 2 of X squared, where does the exponent go according to the power property?

• It is moved to the base of the logarithm

• It is eliminated

• It remains unchanged

• It is placed in front of the logarithm

How do we expand 5x cubed Y using logarithms?

• By dividing the logarithms of 5, x cubed, and Y

• By multiplying the logarithms of 5, x cubed, and Y

• By subtracting the logarithms of 5, x cubed, and Y

• By adding the logarithms of 5, x cubed, and Y

What does the square root in a logarithm imply when expanding?

• A division by 2

• A multiplication by 2

• An exponent of 1/2

• An exponent of 2

When condensing logarithms, what does subtraction inside the logarithm imply?

• No operation outside the logarithm

• Division outside the logarithm

• Multiplication outside the logarithm

• Addition outside the logarithm

In the final example, how is the expression X plus two squared times X simplified?

• X plus 4X plus 4

• X cubed plus 2X squared plus 4

• X cubed plus 4X squared plus 4X

• X squared plus 4X plus 4