How to Calculate Logarithm: A Step-by-Step Guide
Calculates logarithms in any base.
These calculations come up in school, at work and in daily life, from PSLE and O-Level practice to measuring a room for new flooring. Doing them by hand builds understanding, and a calculator lets you check the answer instantly.
What you need
- Number
- Base
Step by step
- Enter the number.
- Enter the base.
- The results update as you type, or press Calculate.
- Read the log_b(x) first, then the supporting figures below it.
The formula
log_b(x) = ln(x) ÷ ln(b).
Worked example
For example, with these inputs:
- Number: 1,000
- Base: 10
the calculator returns:
- log_b(x): 3
- Natural log ln(x): 6.9078
A second example
Now change the inputs to:
- Number: 1,250
- Base: 10
the calculator returns:
- log_b(x): 3.0969
- Natural log ln(x): 7.1309
Practical tips
- Check your answer by working backwards from the result.
- Use brackets to make the order of operations explicit.
- Round only at the final step to avoid accumulated rounding errors.
- For exam work, show your method; marks are often given for working, not just the answer.
Background
A quick mental estimate before calculating is a powerful check. If a room's floor area comes out at 4,000 square metres or a percentage comes out above 100% when it should not, you know to look again.
Each formula has assumptions built in. Area formulas assume flat shapes, volume formulas assume regular solids and statistical measures assume the data you enter is the data you want to describe. Knowing the assumptions helps you pick the right tool.
These calculations appear throughout the Singapore syllabus, from primary school percentages and fractions to secondary school algebra and geometry. Understanding the formula makes problem sums easier because you can recognise which quantity is missing.
Related calculations
- Area of an Ellipse Calculator: Calculates the area of an ellipse from the measurements you enter.
- Area of a Rhombus Calculator: Calculates the area of a rhombus from the measurements you enter.
- Area of a Sector Calculator: Calculates the area of a sector from the measurements you enter.
- Circumference of a Circle Calculator: Calculates the circumference of a circle from the measurements you enter.
Want to skip the arithmetic? The free Logarithm Calculator does all of this instantly and updates as you type.
Run your own numbers: Logarithm Calculator