# Online Logarithm calculator

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# Logarithm Calculator

Calculate logarithm of a number to any base:

* Use e for scientific notation. E.g: 5e3, 4e-8, 1.45e12

When:

*b ^{ y} = x*

Then the base b logarithm of a number x:

log* _{b }x* =

*y*

## Anti-logarithm calculator

In order to calculate log^{-1}(y) on the calculator, enter the base b (10 is the default value, enter e for e constant), enter the logarithm value y and press the = or *calculate* button:

### Logarithm Calculator

The Log (Logarithm) Calculator is used to calculate the logarithm log_{b}x for a base b and a number x. Logarithm (LOG) calculator is an online math calculator that calculates the log value for the positive real number with respect to the given or natural base values (positive, not equal to 1). Using this calculator, we will understand methods of how to find the logarithm of any number with respect to the given base.

It is necessary to follow the next steps:

1.Enter the number and the base of logarithm. These values must be positive real numbers or parameter. The base of logarithm can not be 1.

2. Press the "CALCULATE" button to make the computation.

3. Logarithm calculator will give the logarithm of the positive real number number with the positive base not equal to 1.

** Logarithm definition**

The logarithm of a number x with respect to base b is the exponent to which b has to be raised to yield x. In other words, the logarithm of y to base b is the solution y of the following equation:

b^{y} = x

And for any x and b, there is:

x = log_{b}b^{x}

The logarithm to base b = 10 is called the common logarithm and has many applications in science and engineering. The natural logarithm has the constant e (approximately equal to 2.718281828) as its base. The binary logarithm uses base b = 2 and is prominent in computer science.

** What is Log?**

The logarithm, or log, is the inverse of the mathematical operation of exponentiation. This means that the log of a number is the number that a fixed base has to be raised to in order to yield the number. Conventionally, log implies that base 10 is being used, though the base can technically be anything. When the base is e, ln is usually written, rather than log_{e}. log_{2}, the binary logarithm, is another base that is typically used with logarithms. If for example:

x = b^{y}; then y = log_{b}x; where b is the base

Each of the mentioned bases are typically used in different applications. Base 10 is commonly used in science and engineering, base e in math and physics, and base 2 in computer science.

** Logarithm rules**

Logarithm product rule

log_{b}(x × y) = log_{b}(x) + log_{b}(y)

Logarithm quotient rule

log_{b}(x / y) = log_{b}(x) - log_{b}(y)

Logarithm power rule

log_{b}(x ^{y}) = y × log_{b}(x)

Logarithm base switch rule

log_{b}(c) = 1 / log_{c}(b)

Logarithm change of base rule

log_{b}(x) = log_{c}(x) / log_{c}(b)