Logarithmic equation
Solve logₐx = y for any unknown (base, argument or result), with steps.
Fill in two values and leave the third (e.g. result y) empty – it will be computed.
Fill in two of the three values – the remaining one is computed.
How to solve a logarithmic equation
The basic logarithmic equation logₐx = y links three values: the base a, the argument x, and the result y. Depending on which one you're looking for, a different manipulation is used – all of them come from the relationship between logarithms and powers:
logₐx = y ⟺ aʸ = x
- looking for y y = log x / log a (change of base)
- looking for x x = aʸ (remove the logarithm)
- looking for a a = x^(1/y) (the y-th root of x)
Example: log₂x = 3 means 2³ = x, so x = 8. Or log_a 8 = 3 means a³ = 8, so a = 2. The calculator recognises which field you leave empty and computes it.
Note: base a must be positive and different from 1, argument x must be positive. Not every combination has a real solution.