# How to expand a logarithm?

#### Understand the Problem

The question is asking us to explain the process of expanding a logarithm, which typically involves utilizing logarithmic properties such as the product, quotient, and power rules to rewrite a logarithmic expression in a more expanded form.

Expanded form depends on initial expression.

The final expanded form of the logarithm depends on the initial expression given.

#### Steps to Solve

1. Identify the components inside the logarithm

Identify the terms inside the logarithm that need to be expanded. These could be products, quotients, or powers.

1. Apply the product rule

If you have a product inside the logarithm, you can use the product rule: $$\log_b(xy) = \log_b(x) + \log_b(y)$$

1. Apply the quotient rule

If you have a quotient inside the logarithm, you can use the quotient rule: $$\log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y)$$

1. Apply the power rule

If you have a power inside the logarithm, you can use the power rule: $$\log_b(x^y) = y \cdot \log_b(x)$$

1. Rewrite the logarithm in expanded form

Combine all the applied rules to write the logarithm in its expanded form.

The final expanded form of the logarithm depends on the initial expression given.