Quick guide
How to use this calculator
- Choose a calculation mode when the page offers more than one relationship.
- Enter the labelled known values.
- Read the primary result and use the check or equivalent form to verify its meaning.
Calculation method
Apply the exponent, root, or logarithm relationship
log_b(v)=e exactly when b^e=v.
The calculator checks real-number domains, zero denominators, unsupported powers, and finite-range limits before reporting a result.
Worked example
Worked example
log₂(32)=5 is equivalent to 2^5=32.
log_b(v)=e exactly when b^e=v.
Supported inputs
Precision and limits
Real-number scope
These calculators return real results. Complex branches are handled by the separate complex-number calculators.
Numerical range
Inputs may be zero or have absolute magnitude from 1e-100 through 1e100. Exact integer radical simplification uses its narrower disclosed bound.
Precision
Numerical functions use double-precision arithmetic and normally display 12 significant digits. Symbolic labels are exact only where explicitly stated.
Calculator-specific rule
In logarithmic-to-exponential mode, the entered value is not needed; the equivalent value is calculated from the base and exponent.