Learn how to expand a logarithmic expression with three terms

The video tutorial explains how to expand a logarithmic expression using the product and power rules. The instructor starts with an example involving log base two of seven YX squared, demonstrating the separation of terms using the product rule. Then, the power rule is applied to further simplify the expression. The final expanded form is presented as log base two of seven plus log base two of Y plus two times log base two of X.

What is the initial expression given in the example?

• log base two of seven YX squared

• log base two of seven Y squared

• log base ten of seven Y squared

• log base ten of seven YX squared

What is the first step in expanding the logarithmic expression?

• Convert the base of the logarithms

• Apply the power rule to all terms

• Separate the logarithms using the product rule

• Combine all terms into a single logarithm

Which rule allows you to bring down the exponent in front of the logarithm?

• Power Rule

• Quotient Rule

• Change of Base Rule

• Product Rule

What is the expanded form of log base two of X squared?

• log base two of 2X

• log base two of X squared

• 2 times log base two of X

• log base two of X

What is the final expanded expression?

• log base two of seven plus log base two of Y plus log base two of X squared

• log base two of seven plus 2 times log base two of Y plus log base two of X

• log base two of seven plus log base two of Y plus 2 times log base two of X

• log base two of seven plus log base two of Y plus log base two of X