Log Calculator (Logarithm)
Please provide any two values to calculate the third in the logarithm equation logbx=y. It can accept "e" as a base input.
What is Log?
A logarithm (log) reverses the process of exponentiation. In other words, the logarithm of a value tells you which exponent you must apply to a chosen base to obtain that value. By default the term log refers to base‑10, but any base is permissible. When the base is the natural constant e, the notation ln is preferred to loge. The base‑2 logarithm, also known as the binary log, is another common choice. For instance:
x = by; then y = logbx; where b is the base
The various bases serve distinct practical purposes. Base‑10 appears frequently in scientific and engineering contexts, the natural base e is predominant in mathematics and physics, while base‑2 is the standard in computing.
Basic Log Rules
When the argument of a logarithm is the product of two numerals, the logarithm can be re-written as the addition of the logarithm of each of the numerals.
logb(x × y) = logbx + logby
EX: log(1 × 10) = log(1) + log(10) = 0 + 1 = 1
When the argument of a logarithm is a fraction, the logarithm can be re-written as the subtraction of the logarithm of the numerator minus the logarithm of the denominator.
logb(x / y) = logbx - logby
EX: log(10 / 2) = log(10) - log(2) = 1 - 0.301 = 0.699
If there is an exponent in the argument of a logarithm, the exponent can be pulled out of the logarithm and multiplied.
logbxy = y × logbx
EX: log(26) = 6 × log(2) = 1.806
It is also possible to change the base of the logarithm using the following rule.
| logb(x) = |
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| EX: log10(x) = |
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To switch the base and argument, use the following rule.
| logb(c) = |
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| EX: log5(2) = |
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Other common logarithms to take note of include:
logb(1) = 0
logb(b) = 1
logb(0) = undefined
limx→0logb(x) = - ∞
ln(ex) = x