Logarithmic Properties and Exponents

The video tutorial explains how to expand logarithmic expressions using log properties. It covers the product, power, and quotient properties of logarithms, demonstrating how to apply these properties to simplify expressions. The tutorial uses examples to illustrate the process, including converting roots to rational exponents and moving exponents to coefficients. The goal is to expand expressions as much as possible, providing a clear understanding of logarithmic expansion techniques.

What is the first step in expanding a logarithmic expression using log properties?

• Simplify the expression

• Directly apply the power property

• Use rational exponents

• Apply the quotient property

How do you express the cube root of a variable using rational exponents?

• Raise the variable to the power of 3

• Raise the variable to the power of 1/3

• Multiply the variable by 3

• Divide the variable by 3

Which property of logarithms is used to expand log base a of a product?

• Product property

• Inverse property

• Power property

• Quotient property

What is the result of applying the product property to log base a of m times n?

• log base a of m times log base a of n

• log base a of m divided by log base a of n

• log base a of m plus log base a of n

• log base a of m minus log base a of n

How do you apply the power property of logarithms to log base a of n to the power of p?

• Divide the log by p

• Add p to the log

• Multiply the log by p

• Subtract p from the log

What is the expanded form of log base a of x to the twelfth?

• log base a of x plus 12

• 12 times log base a of x

• log base a of x divided by 12

• log base a of x times 12

What is the first step in expanding a natural logarithm expression with a quotient?

• Apply the quotient property

• Apply the product property

• Use the power property

• Simplify the expression

How do you express the square root of a variable using rational exponents?

• Raise the variable to the power of 1/2

• Multiply the variable by 2

• Raise the variable to the power of 2

• Divide the variable by 2

What is the expanded form of natural log of x to the fifth?

• Natural log of x divided by 5

• Natural log of x plus 5

• 5 times natural log of x

• Natural log of x times 5

What is the final step in expanding a logarithmic expression using the power property?

• Divide the exponents

• Move each exponent to the position of the coefficient

• Add the exponents

• Subtract the exponents