Laws of Logarithms
Convert products to sums, powers to multiples.
Key idea
Convert products to sums, powers to multiples.
In depth
log(xy) = log x + log y, log(x/y) = log x − log y, log(xⁿ) = n log x. They mirror the exponent laws because logs are exponents.
Worked example
log₂(8·4) = log₂8 + log₂4 = 3 + 2 = 5.
Formula
Real-world uses
- Simplifying growth formulas and turning multiplication into addition in scientific calculations
Common mistake
Writing log(x + y) = log x + log y. Only products split.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Laws of Logarithms?
Convert products to sums, powers to multiples. It is a topic at the advanced level in Algebra.
What is the formula for Laws of Logarithms?
The key formula is log(xy) = log x + log y.
Where is Laws of Logarithms used in real life?
Real-world examples: Simplifying growth formulas and turning multiplication into addition in scientific calculations.
What should I learn before Laws of Logarithms?
Make sure you are comfortable with Logarithms, the previous topic in Algebra.
What is a common mistake with Laws of Logarithms?
Writing log(x + y) = log x + log y. Only products split.
How can I practise Laws of Logarithms?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Laws of Logarithms?
Move on to Change of Base Formula next.
Related advanced topics in Algebra
- Absolute Value Inequalities – Rewrite as a compound inequality.
- Systems with Three Variables – Reduce to two variables then solve in sequence.
- Systems of Inequalities – Solution region is the overlap of half-planes.
- Factoring by Grouping – Group terms in pairs to find a common binomial.
- Sum and Difference of Cubes – Special factoring patterns for cubes.
- Completing the Square – Rewrite a quadratic as a perfect square plus constant.