Logarithms Calculator
Calculate logarithms with any base. Supports natural logarithms (ln), common logarithms (log₁₀), and custom base logarithms.
Enter a positive number to calculate its logarithm
Enter a positive base value (not equal to 1)
Ready to Calculate
Enter your values and click Calculate to see results
Logarithm Value
Type
Antilogarithm
Formula
Additional Information
Natural Logarithm (ln)
Common Logarithm (log₁₀)
Binary Logarithm (log₂)
Important Assumptions
The input number must be positive (greater than 0).
The base must be positive and not equal to 1.
Frequently Asked Questions
What is the difference between natural and common logarithms?
Natural logarithms (ln) use e (≈ 2.718) as the base; common logarithms (log₁₀) use 10.
Can I calculate logarithms of negative numbers?
No. Logarithms are only defined for positive real numbers.
Why is the base of a logarithm important?
The base determines the number system and application context (e.g., base 10 vs base e).
How do I convert between different logarithm bases?
Use the change of base formula: log_b(x) = log_a(x) / log_a(b).
What are some practical applications of logarithms?
Earthquake intensity (Richter), pH in chemistry, sound intensity (dB), population growth, finance.