Logarithmic Properties and Simplifications

The video tutorial explains how to use properties of logarithms to simplify expressions. It covers the product property for combining logs with the same base, the quotient property for logs with a difference, and the power property for logs with coefficients. Examples include simplifying expressions with common logs, log base 7, and natural logs, demonstrating how to apply these properties step-by-step.

What property of logarithms is used to combine log base A of m plus log base A of n?

• Quotient Property

• Product Property

• Power Property

• Change of Base Property

If you have log base 12 of 5x plus log base 12 of 2x squared, what is the combined expression?

• log base 12 of 10x

• log base 12 of 10x cubed

• log base 12 of 10x squared

• log base 12 of 7x cubed

Which property of logarithms is used when you have a difference of two logs with the same base?

• Product Property

• Quotient Property

• Power Property

• Change of Base Property

What is the simplified form of log of 40x^3y^2 minus log of 12xy^4?

• log of 10x^3/3y^2

• log of 10x^2/3y^2

• log of 10x^2/4y^2

• log of 10x^3/4y^2

What should be applied first when the coefficients of logs are not equal to one?

• Change of Base Property

• Quotient Property

• Product Property

• Power Property

What is the result of applying the power property to 2 log base 7 of 3x?

• log base 7 of 3x

• log base 7 of 6x

• log base 7 of 9x^2

• log base 7 of 3x^2

After applying the power property, what is the combined expression for two log base 7 of 3x plus three log base 7 of 4?

• log base 7 of 576x^2

• log base 7 of 576x^4

• log base 7 of 576x

• log base 7 of 576x^3

What is the first step in simplifying five natural log 2x minus two natural log 3x?

• Apply the product property

• Apply the quotient property

• Apply the power property

• Apply the change of base property

What is the simplified form of natural log of 32x^5 minus natural log of 9x^2?

• natural log of 32x^3/8

• natural log of 32x^4/9

• natural log of 32x^2/9

• natural log of 32x^3/9

What is the common factor between 32 and 9 in the expression natural log of 32x^5 divided by 9x^2?

• 4

• 2

• 3

• 1