📈 Log & Exponent Calculator
Two calculators, updating live as you type.
Logarithm: logb(x)
Exponent: bx
One change-of-base line does all the work
Browsers only expose a natural logarithm, so every base you ask for is derived from it, and the exponent panel is a straight power:
log b(x) = ln(x) / ln(b)
b x = pow(b, x)The defaults, x = 1000 and b = 10, give 3, because ln(1000) = 6.90775528 divided by ln(10) = 2.30258509 is exactly 3. The same panel also prints ln(1000), log₁₀(1000) = 3 and log₂(1000) = 9.96578428. The exponent panel starts at 2 and 10, which is 1024.
Which logarithm you actually want
- ln, base e (2.718282), is the one in growth, decay and half-life work.
- log₁₀ is the scale behind pH, decibels and earthquake magnitudes - each whole step is a factor of ten.
- log₂ counts doublings and bits. 9.97 for 1000 means you need 10 bits to hold a thousand distinct values.
- Fractional exponents are roots. 2 to the power 0.5 is 1.41421356, the square root of 2, and a negative exponent gives the reciprocal: 2 to the -3 is 0.125.
Frequently asked questions
What is log base 2 of 1000?
9.96578428. It sits just under 10 because 2 to the tenth is 1024, slightly more than 1000.
What is the difference between log and ln?
ln is base e, about 2.718282. Written on its own, log usually means base 10. The logarithm panel shows both alongside whatever base you type.
Why will it not accept a base of 1?
Every power of 1 is 1, so no exponent turns 1 into anything else. In the formula that shows up as a division by ln(1), which is zero.