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Logarithm Calculator

The logarithm calculator can calculate any logarithm base and the number of which can be represented by natural numbers, fractional numbers, and expressions containing many operations and functions.


Select the base of the logarithm, or enter the value of the base


How to Calculate Logarithms

The logarithm is denoted as loga b and this entry reads as: The logarithm of x to base b

When calculating logarithms, keep in mind that the numbers a and b must be greater than 0 and a must not be equal to 1.

loga b exists for a> 0, a โ‰  1, b> 0

Logarithms with base a equal to 2, 10 or number e got their names:

loge b whose base is equal to Euler's number e (e = 2.7182818284 ...) is called - Natural logarithm and is denoted ln b . For example, ln 4 is the same as loge 4, but the ln entry itself says that the base is โ€‹โ€‹e and therefore the notation is shortened.

log10 b whose base is 10 is called Common logarithm and is denoted lg b . For example, lg 6, which is the same as log10 6

log2 b whose base is 2 is called Binary logarithm and is denoted lb b , such logarithms are often used in computer science. For example, lb 3 is the same as log2 3.

You can easily determine whether the logarithm loga b is negative or positive, for this there is a rule: if 0 < a > 1 and 0 < b <1 or 0 < a <1 and 0 < b > 1 then the logarithm is negative, otherwise positive

loga b <0 if 0 < a > 1 and 0 < b <1 or 0 < a <1 and 0 < b > 1

For example, these logarithms will be negative log1/3 4, log4 1/3, log2/3 5, log5 2/3, etc. That is, either a or b must be less than one, but not both.

Calculating the logarithm means finding the exponent to which the number a must be raised to get the number b. In simple terms, when we calculate the logarithm, we always find the power, and if we raise the number a to this power, we get the number b.

Let's denote x as the unknown power of a, then we can write the following equation: a x = b

Here are some examples:
Given the logarithm of log4 64, we need to find such an exponent that when raising the number 4 to it we should get 64. Let's write the equation:
4 x = 64 < br /> 4 x = 4 3
x = 3
Let's check, raise the number 4 to the power of 3: 4 3 = 64.

In general, any value of the logarithm is always easy to check, it is enough to raise the number a to a power equal to the value of the logarithm, and if the result is equal to the number b, then the answer is correct.

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