Example 1 — base 2
- Number: 8
- Base: 2
3
Because 2³ = 8.
Logarithm
Enter a number and a base. The answer is: “to which power should I raise the base to get this number?”
A logarithm undoes exponentiation. You are not asking “what is 10 squared?”, but “to which power should I raise 10 to get 100?”. Answer: 2. The base must be positive and not 1, and the number must be positive too.
Result
Enter a number and a base to see the result.
What it means
Take 100 with base 10. Ask: 10 to which power is 100? 10² = 100, so the logarithm is 2.
School notation: log10 100 = 2. Base 10 is a common decimal log; base e is the natural log. Here you can use any valid base.
A fractional answer just means you need a non-whole power — that is fine.
Where it helps
- School work on powers and logs.
- Checking “which power gives this number?”.
- Thinking about orders of magnitude in a simple school way.
- Moving between multiplying powers and adding exponents.
How to use it
- Enter the number you want the log of (must be greater than zero).
- Enter the base (greater than zero and not 1 — not 1, not 0, not negative).
- Read the result: that is the exponent.
Examples
Example 2 — base 10
- Number: 1000
- Base: 10
3
Because 10³ = 1000.
Example 3 — negative result
- Number: 0.25
- Base: 2
−2
Because 2⁻² = 0.25. A negative result means a negative power.
FAQ
What is a logarithm in plain words?
The answer to: to which power should I raise the base to get this number?
Why must the number be positive?
With the usual school rules, a positive base (not 1) does not give zero or negatives.
Why can’t the base be 1?
Because 1 to any power stays 1. You cannot reach other targets.
Can the base be a fraction like 0.5?
Yes, if it is positive and not 1.
How is a log different from a power?
Power: you know base and exponent, find the value. Log: you know base and value, find the exponent.
What does a negative result mean?
You need a negative power, which means division. Example: log₁₀ 0.01 = −2.
Can I take the log of 1?
Yes. For any valid base, log of 1 is 0, because base⁰ = 1.
Why reject a base very close to 1?
The calculation becomes unstable and easy to misread. The base must be clearly different from 1.