Log Calculator (Logarithm)
Type 8 with base 2 into most tools and you get 3.0000000. The answer is 3. Not almost 3 — exactly 3, and writing it with a tail of zeros suggests a rounding that never happened.
That is where this log calculator starts. When the answer is a whole number or a simple fraction it is given as one, and when it genuinely cannot be, the value is rounded to ten places and the calculator says so in words. You always know which of the two you are looking at — which is more than most tools will tell you, however carefully they calculate the logarithm itself.
What This Log Calculator Does With the Base
Almost every question about how to do logarithms on a calculator comes down to the base. The log key means base 10. The ln key means base e. They are different keys because they are different questions, and a great many marks are lost to that one confusion — which is why so many people end up searching how to use log on calculator rather than for the answer itself.
So this log calculator puts the base at the top as four buttons — log10, ln, log2, or any base you type — with a line underneath saying which one is active. Tap one and the answer changes in place. Base 2 is one press, so this doubles as a log base 2 calculator without your going anywhere else, and the same is true of every other base a logarithms calculator is normally asked for. The same number, three bases, three answers:
log 100 is 2. ln 100 is 4.6051701860. log2 100 is 6.6438561898. Nothing about the 100 changed; only the base did.
A Logarithm Calculator for All Three Unknowns
A logarithm ties three things together: logb x = y. Give any two and the third follows, and this logarithm calculator will find whichever one you are missing. Most a logarithmic calculator will do is the first of those three; here all three are one tap apart.
Leave y unknown and it is an ordinary logarithm. Leave x unknown and you are after an antilogarithm — the number rather than the power — which is just the base raised to y. Leave b unknown and it becomes a root: if b³ = 1000 then b is 10.
Pick which one you want at the top and the boxes you do not need disappear. There is no guessing at which field to leave blank, which is the part a log calculator usually leaves you to work out for yourself.
Change of Base — a Log Calculator for Any Base
There is no key on any calculator for log base 5. What there is instead is the change-of-base formula, and it is the reason a natural logarithm calculator can answer a question about base 5 at all: log5 20 is the same as ln 20 divided by ln 5. That single division is what turns a natural log calculator into one for every base.
Choose any base here and that division appears in the working with both natural logs filled in, so you can follow it on paper rather than trusting a black box. Base 10 works equally well on top and bottom — what matters is only that it is the same base in both places.
Tap once under the answer and this log calculator shows the same number in all three common bases at once, which is the quickest way to see how much the base matters. Under that is the working step by step: what the question is actually asking, then either the exact power or the rounding, and the identity read back the other way as a check.
Fractions, decimals, e, and numbers written with commas or in scientific notation all go straight in. Anything that cannot be a logarithm — zero, a negative number, base 1 — is refused with the reason rather than a blank screen. It is free to use online, with no account.
Log Calculator FAQ
How do you do log on a calculator?
What is the difference between log and ln?
How do you find a logarithm with any base?
How do you use logarithms in calculator work generally?
What is an antilogarithm?
Check the base first, then read whether the answer is exact or rounded. Whatever log calculator you end up using, those two habits cover most of what goes wrong with logarithms.