Log Calculator (Logarithm)
Solve log_b(x) = y for the base, the number or the logarithm; natural and base-10 logs, exact where possible.
Change the values and press Calculate to work out your own figures.
Fill in two of base, number and logarithm; leave the third blank. Use e for the natural log.
Show the working
- log_b(x) = ln(x) ÷ ln(b) = ln(8) ÷ ln(2) = 3
How to use it
Fill in two of base, number and logarithm; leave the third blank. Use e for the natural log.
Number boxes accept whole numbers, decimals, fractions (3/4), powers (2^10), roots (sqrt(2)) and the constants pi and e. Show the working lists the steps.
Key facts
y = ln x ÷ ln b; x = bʸ; b = x^(1/y)
Rules
log_b 1 = 0, log_b b = 1, and log_b of 0 or a negative number is undefined.
Questions
What is log₂ 8?
3.
What is ln 10?
2.30258509299.
Formulas
y = ln x ÷ ln b; x = bʸ; b = x^(1/y)
Sources
Limitations
- Expressions up to 500 characters; matrices up to 10 × 10.
- Big-number results up to 100,000 digits; factorials up to 10,000!.
- Numbers in words up to 10^102 (short scale).