Log Calculator · Practical guide
How to Find the Inverse of a Logarithm
Undo any logarithm with one exponentiation — and check every result with the inverse row of the calculator above.
At a glance
The Rule
The inverse of a logarithm is exponentiation. If log_b(x) = y, then b^y = x. That single rule undoes every logarithm, in every base. For example, log10(1000) = 3, so the inverse is 10^3 = 1,000. The calculator above displays the inverse — b raised to your result — on every calculation, so the round-trip check is built in.
Interactive tool
Log Calculator
Enter your own values, then compare the result with the examples below.
Results
Worked Examples
| Logarithm | Result | Inverse (check) |
|---|---|---|
| log10(1,000) | 3 | 10^3 = 1,000 |
| ln(5) | 1.609438 | e^1.609438 = 5 |
| log2(256) | 8 | 2^8 = 256 |
| log5(125) | 3 | 5^3 = 125 |
Solving Logarithmic Equations
To solve an equation like log10(x) = 2.5, apply the inverse to both sides: x = 10^2.5 = 316.23 (approximately). Sanity-check: 10^0.5 = 3.16228, and 3.16228 x 100 = 316.228. For natural log equations like ln(x) = 2, the inverse gives x = e^2 = 7.389056.
Why the Inverse Matters
Logarithms and exponentiation cancel each other, which is what makes logs useful: they turn multiplication into addition and powers into multiplication. Whenever a log result looks surprising, raise the base to it — if you land back on your original number, the logarithm is right.
Frequently Asked Questions
What is an antilog?
Antilog is the traditional name for the inverse of a logarithm. The antilog of y in base b is simply b^y.
What is the inverse of the natural log?
The inverse of ln(x) is e^x. If ln(x) = y, then e^y = x.
What is the inverse of log base 10?
The inverse is 10^x. If log10(x) = y, then 10^y = x.
Does the calculator show the inverse automatically?
Yes. Every result includes an inverse row showing b raised to the calculated logarithm, which equals your original number.