Log Functions in Python

In this tutorial, we are going to learn about the logarithmic functions from math module. We have four variants of logarithmic functions. Pythons' provides all of them in the math module. Let's learn about them one by one.

math.log(number, [Base])

The math.log(number, [Base]) method is used to compute the logarithm of any Base. If we didn't specify any base value, then it will take e as default base.

Note − You will get ValueError if you pass a negative number to the method.

Example

Let's see some examples.

 Live Demo

# importing math module
import math
# logarithm with base 3
print(math.log(15, 7))

Output

If you run the above program, you will get the following result.

1.3916625094004957

You can specify any base value you want in the above program. Let's see the same example without any base value. Default base value is e.

Example

 Live Demo

# importing math module
import math
# logarithm with base e(default)
print(math.log(15))

Output

If you run the above code, you will get the following results.

2.70805020110221

Example

Let's see what happens if we pass negative number to the math.log() method.

 Live Demo

# importing math module
import math
# logarithm with negative number
print(math.log(-15))

Output

If you run the above program, you will get the following results.

---------------------------------------------------------------------------
ValueError                   Traceback (most recent call last)
<ipython-input-6-b686fcb806c6> in <module>
      3
      4 # logarithm with base e(default)
----> 5 print(math.log(-15))
ValueError: math domain error

math.log2(number)

If you want to compute logarithm for base 2 value, then we can use math.log2() method. It's similar to the above method. Let's see some examples.

Example

 Live Demo

# importing math module
import math
# logarithm with base 2
print(math.log2(15))

Output

If you run the above code, you will get the following results.

3.9068905956085187

Similar to the math.log method, we will get an error if we pass a negative number to the math.log2 method. Let's see it with the example.

Example

 Live Demo

# importing math module
import math
# logarithm with base 2 & negative number
print(math.log2(-15))

Output

If you see the output of the program by executing it, then you will find that the error we got now and before is the same.

---------------------------------------------------------------------------
ValueError                               Traceback (most recent call last)
<ipython-input-3-8019b45e571f> in <module>
      3
      4 # logarithm with base 2 & negative number
----> 5 print(math.log2(-15))
ValueError: math domain error

math.log10(number)

We can find the logarithm with base 10 using the math.log10 method. It's similar to the above math.log2 method. Let's see some examples.

Example

 Live Demo

# importing math module
import math
# logarithm with base 10
print(math.log10(15))

Output

If you execute the above program, you will get the following output.

1.1760912590556813

Try to pass a negative number to the math.log10 method. You will get an error similar to the above methods.

Example

 Live Demo

# importing math module
import math
# logarithm with base 10 & negative number
print(math.log10(-15))

Output

If you see the output you will get the following error.

---------------------------------------------------------------------------
ValueError                            Traceback (most recent call last)
<ipython-input-5-52ac56b802ca> in <module>
      3
      4 # logarithm with base 10 & negative number
----> 5 print(math.log10(-15))
ValueError: math domain error

math.log1p(number)

The method math.log1p(x) will compute log(1 + x) with base e. It computes logarithm of given number by adding 1 to it. Let's see some examples.

Example

 Live Demo

# importing math module
import math
# logarithm
print(math.log1p(15)) # similar to math.log(16)

Output

If you execute the above program, you will get the following results.

2.772588722239781

Try to pass a negative number to the math.log1p method. I'm sure that you will get an error as we have seen before.

Example

 Live Demo

# importing math module
import math
# logarithm
print(math.log1p(-15))

# importing math module import math # logarithm print(math.log1p(-15))

Output

We'll get the following error because of the negative number that we passed to the method.

---------------------------------------------------------------------------
ValueError                      Traceback (most recent call last)
<ipython-input-15-26016884cb23> in <module>
      3
      4 # logarithm
----> 5 print(math.log1p(-15))
ValueError: math domain error

Conclusion

We've seen a total of four logarithm methods from the math module. We'll get an error if we pass negative number to any of the logarithmic methods seen in the tutorial. And you can pass floating numbers to the methods as well. Try to execute the examples seen in this tutorial with floating numbers.