Learn how to expand logarithmic expressions using the product rule

The video tutorial explains how to expand logarithms by using the product and power rules. It begins with an introduction to the concept of expanding a single logarithm into multiple logarithms. The instructor demonstrates the application of the product rule to separate terms by addition while maintaining the same base. Finally, the power rule is applied to simplify terms with exponents, resulting in a fully expanded logarithmic expression.

What is the process of expanding a logarithm?

• Simplifying a logarithm to a single number

• Combining multiple logarithms into one

• Going from one logarithm to multiple logarithms

• Changing the base of a logarithm

When separating terms in a logarithm expression with multiplication, what operation is used?

• Multiplication

• Addition

• Division

• Subtraction

What must remain the same when using the product rule to expand logarithms?

• The variables

• The exponents

• The coefficients

• The bases

How is an exponent handled when applying the power rule to a logarithm?

• It is added to the base

• It is divided by the base

• It is multiplied by the base

• It is brought down in front of the logarithm

What is the final expanded form of log base 10 of 7 + 3 times log base 10 of X?

• log base 10 of 7 * log base 10 of X^3

• log base 10 of 7 + 3 log base 10 of X

• log base 10 of 7 + log base 10 of X^3

• log base 10 of 7 * 3 log base 10 of X