How this calculator works
A logarithm finds the exponent that produces a given positive number. Base 2 logarithms measure how many doublings produce a number and are common in binary arithmetic. The inverse mode raises the base to the entered logarithm. Zero and negative arguments have no real logarithm.
Formula
y = log_2(x); x = 2^y.
Worked example
log_2(1024) = 10 because ten doublings of one give 1024. log_2(1/8) = -3.
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Frequently asked questions
Can the answer be negative?
The logarithm may be negative, but a power of a positive base is always positive.
What happens at one?
Every valid logarithm of one is zero. Raising a valid base to zero gives one.
How precise is the answer?
Calculations use standard floating-point arithmetic. The displayed result has up to ten decimal places, and overflow or underflow produces an error.