Expanding logarithmic expressions

The video tutorial explains how to expand a natural logarithm by using the properties of logarithms. It begins with the concept of the difference of two properties and demonstrates how to break a logarithm into a difference of two separate logarithms. The tutorial then applies the power rule, showing how to rewrite a logarithm with a power in front. The video concludes with a summary of the steps involved in expanding a natural logarithm.

What is the initial step when dealing with the difference of two properties in a logarithm?

• Ignore the difference

• Multiply them together

• Break them into two separate logarithms

• Combine them into a single logarithm

When breaking down a natural logarithm, what is the base used?

• 10

• 5

• 2

• e

In the example given, what is the expression for the natural logarithm of Z to the third power?

• Ln(Z) + 3

• Ln(Z^3)

• Ln(3Z)

• 3 * Ln(Z)

How is the power rule applied to the logarithm Ln(Z^3)?

• The power is added to the logarithm

• The power is multiplied by the logarithm

• The power is moved to the front of the logarithm

• The power is subtracted from the logarithm

What is the final expanded form of the natural logarithm in the example?

• Ln(1) * Ln(Z^3)

• 3 * Ln(1) - Ln(Z)

• Ln(1) - 3 * Ln(Z)

• Ln(1) + 3 * Ln(Z)