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.
Answer
Expanded form depends on initial expression.
Answer for screen readers
The final expanded form of the logarithm depends on the initial expression given.
Steps to Solve
- Identify the components inside the logarithm
Identify the terms inside the logarithm that need to be expanded. These could be products, quotients, or powers.
- Apply the product rule
If you have a product inside the logarithm, you can use the product rule: $$\log_b(xy) = \log_b(x) + \log_b(y)$$
- Apply the quotient rule
If you have a quotient inside the logarithm, you can use the quotient rule: $$\log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y)$$
- Apply the power rule
If you have a power inside the logarithm, you can use the power rule: $$\log_b(x^y) = y \cdot \log_b(x)$$
- 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.
More Information
Expanding a logarithm helps to simplify complex logarithmic expressions and can aid in solving logarithmic equations.
Tips
A common mistake is to forget to apply all the logarithmic properties or to apply them incorrectly. Make sure to review and apply each rule carefully.
