Change of Base Formula
Convert logs between bases.
Key idea
Convert logs between bases.
In depth
log_b(x) = ln x / ln b, so any logarithm can be computed with a calculator that has only ln or log. It works because both sides satisfy the definition when converted back to exponentials.
Worked example
log₂(10) = ln 10 / ln 2 ≈ 3.3219.
Formula
Real-world uses
- Calculating logarithms in base 2 for computing or base 10 on a standard calculator
Common mistake
Flipping the fraction.
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 Change of Base Formula?
Convert logs between bases. It is a topic at the advanced level in Algebra.
What is the formula for Change of Base Formula?
The key formula is log_b x = ln x / ln b.
Where is Change of Base Formula used in real life?
Real-world examples: Calculating logarithms in base 2 for computing or base 10 on a standard calculator.
What should I learn before Change of Base Formula?
Make sure you are comfortable with Laws of Logarithms, the previous topic in Algebra.
What is a common mistake with Change of Base Formula?
Flipping the fraction.
How can I practise Change of Base Formula?
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 Change of Base Formula?
Move on to Exponential and Log Equations 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.