# Logarithm calculator

log

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## What is a logarithm solver?

A logarithm, often called a log, is essentially the reverse of raising a number to a power. It answers the question: "To what power must we raise a certain base to get a particular number?" Usually, when we say "log" without any base, it means we're using base 10, which is common in science and engineering. But the base can be anything. For instance, when the base is 'e' (a special mathematical constant), we use "ln" instead of "log

*e." In computer science, we often use base 2, or "log2". For example, if we have x = b^y, then y is the log value of x with base b, written as y = log*b(x). Each base has its preferred uses: base 10 in science, base e in mathematics and physics, and base 2 in computer science. When using a log solver, these different bases can be specified to calculate the log base function of a given number.## How do logarithm rules work?

When you take the log of two numbers multiplied together, you can split it into the sum of their logs.

logb(x × y) = logbx + logby

EX: log(1 × 10) = log(1) + log(10) = 0 + 1 = 1

For a fraction, the log becomes the difference between the log of the top number and the bottom number.

logb(x / y) = logbx - logby

EX: log(10 / 2) = log(10) - log(2) = 1 - 0.301 = 0.699

If your log argument is raised to a power, you can bring the exponent out and multiply it.

logbxy = y × logbx

EX: log(26) = 6 × log(2) = 1.806

Changing the base of a log is possible with this formula:

log

_{b}(x) = log_{k}(x) / log_{k}(b)EX: log

_{10}(x) = log_{2}(x) / log_{k}(10)To swap the base and the argument in the log calculation, use this:

log

_{b}(c) = 1/log_{c}(b)EX: log

_{5}(2) = 1 / log_{2}(5)Here are some other log rules to remember when you find log:

log

_{b}(1) = 0log

_{b}(b) = 1log

_{b}(0) = undefinedlim

_{x→0}log_{b}(x) = - ∞In(e

^{x}) = x