Condensing logarithmic expressions

The video tutorial explains how to simplify a logarithmic expression using various rules. It begins with applying the power and product rules, then moves on to the quotient rule. The tutorial further explores exponent properties to simplify the expression into a single logarithm. The process is demonstrated step-by-step, ensuring a clear understanding of each rule and its application.

What is the first step in simplifying the given logarithmic expression?

• Use the power rule

• Combine the logarithms

• Apply the quotient rule

• Expand the expression

How do you rewrite the difference of two logarithms with the same base?

• As a sum

• As a product

• As a quotient

• As a power

Which rule is applied to move the 1/2 in front of the logarithm?

• Product rule

• Quotient rule

• Power rule

• Change of base rule

What property of exponents is used to simplify the expression further?

• Power of a product

• Power of a quotient

• Product of powers

• Quotient of powers

What is the final form of the expression after applying all the rules?

• log base two of X ^3 / Z ^2

• log base two of sqrt X ^3 / Z

• log base two of X ^3 * Z ^2

• log base two of X ^3 + Z ^2