# Log functions in Python

Python offers many inbuild logarithmic functions under the module “math” which allows us to compute logs using a single line. There are 4 variants of logarithmic functions, all of which are discussed in this article.

1. log(a,(Base)) : This function is used to compute the natural logarithm (Base e) of a. If 2 arguments are passed, it computes the logarithm of desired base of argument a, numerically value of log(a)/log(Base).

```Syntax :
math.log(a,Base)
Parameters :
a : The numeric value
Base :  Base to which the logarithm has to be computed.
Return Value :
Returns natural log if 1 argument is passed and log with
specified base if 2 arguments are passed.
Exceptions :
Raises ValueError is a negative no. is passed as argument.
```

 `# Python code to demonstrate the working of ` `# log(a,Base) ` ` `  `import` `math ` ` `  `# Printing the log base e of 14 ` `print` `(``"Natural logarithm of 14 is : "``, end``=``"") ` `print` `(math.log(``14``)) ` ` `  `# Printing the log base 5 of 14 ` `print` `(``"Logarithm base 5 of 14 is : "``, end``=``"") ` `print` `(math.log(``14``,``5``)) `

Output :

```Natural logarithm of 14 is : 2.6390573296152584
Logarithm base 5 of 14 is : 1.6397385131955606
```

2. log2(a) : This function is used to compute the logarithm base 2 of a. Displays more accurate result than log(a,2).

```Syntax :
math.log2(a)
Parameters :
a : The numeric value
Return Value :
Returns logarithm base 2 of a
Exceptions :
Raises ValueError is a negative no. is passed as argument.
```

 `# Python code to demonstrate the working of ` `# log2(a) ` ` `  `import` `math ` ` `  `# Printing the log base 2 of 14 ` `print` `(``"Logarithm base 2 of 14 is : "``, end``=``"") ` `print` `(math.log2(``14``)) `

Output :

```Logarithm base 2 of 14 is : 3.807354922057604
```

3. log10(a) : This function is used to compute the logarithm base 10 of a. Displays more accurate result than log(a,10).

```Syntax :
math.log10(a)
Parameters :
a : The numeric value
Return Value :
Returns logarithm base 10 of a
Exceptions :
Raises ValueError is a negative no. is passed as argument.
```

 `# Python code to demonstrate the working of ` `# log10(a) ` ` `  `import` `math ` ` `  `# Printing the log base 10 of 14 ` `print` `(``"Logarithm base 10 of 14 is : "``, end``=``"") ` `print` `(math.log10(``14``)) `

Output :

```Logarithm base 10 of 14 is : 1.146128035678238
```

3. log1p(a) : This function is used to compute logarithm(1+a) .

```Syntax :
math.log1p(a)
Parameters :
a : The numeric value
Return Value :
Returns log(1+a)
Exceptions :
Raises ValueError is a negative no. is passed as argument.
```

 `# Python code to demonstrate the working of ` `# log1p(a) ` ` `  `import` `math ` ` `  `# Printing the log(1+a) of 14 ` `print` `(``"Logarithm(1+a) value of 14 is : "``, end``=``"") ` `print` `(math.log1p(``14``)) `

Output :

```Logarithm(1+a) value of 14 is : 2.70805020110221
```

Exception

1. ValueError : This function returns value error if number is negative.

 `# Python code to demonstrate the Exception of ` `# log(a) ` ` `  `import` `math ` ` `  `# Printing the log(a) of -14 ` `# Throws Exception ` `print` `(``"log(a) value of -14 is : "``, end``=``"") ` `print` `(math.log(``-``14``)) `

Output :

```log(a) value of -14 is :
```

Runtime Error :

```Traceback (most recent call last):
print (math.log(-14))
ValueError: math domain error
```

Practical Application

One of the application of log10() function is that it is used to compute the no. of digits of a number. Code below illustrates the same.

 `# Python code to demonstrate the Application of ` `# log10(a) ` ` `  `import` `math ` ` `  `# Printing no. of  digits in 73293 ` `print` `(``"The number of digits in 73293 are : "``, end``=``"") ` `print` `(``int``(math.log10(``73293``) ``+` `1``)) `

Output :

```The number of digits in 73293 are : 5
```

This article is contributed by Manjeet Singh. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.