Python math natural log

How to Calculate ln in Python

The ln in Python refers to the logarithm of a number to a given base. This base value when not mentioned is e The ln in Python can be calculated by either the Math.log() method or the Numpy.log() method.

What is the Natural Logarithm?

The natural logarithm is defined as the given number’s logarithm to the base value. The base value in the case of natural logarithm is e .

Representation of Natural Logarithm:

The natural logarithm is often represented as loge(x) or ln(x) . Usually, the e in loge(x) is considered implicit, thus it is represented as log(x).

Following are some unique attributes of natural logarithms:

Where do We use Natural Logarithms?

Natural logarithms are useful when we need to solve problems that include time events or growth events.

How to Calculate ln in Python?

So far we’ve learned what is the natural logarithm. In this section, we will learn how to calculate ln in Python. There are two different methods to calculate ln in Python:

Method1: Use Python math to Calculate the Natural Logarithm (ln)

To calculate the natural logarithm value of a number we can use the log() method of the math library of Python.

Syntax:

• With one argument, return the natural logarithm of x (to base e).
• With two arguments, return the logarithm of x to the given base, calculated as log(x)/log(base).

While using this method if no base value is provided, the value defaults to e, meaning that by only providing a number, you are automatically calculating the natural logarithm.

This may look like something happening not in the way we would expect it to but if we recall from the introduction that in many cases the base e is implicit, thus, many times it is omitted when referring to a log() function without a specified base.

Example

In this example, we will calculate and print the natural logarithm value for different values using the math.log() method.

Explanation of the example:

In the above example, we take the values e, 1 , and 10 and pass the values to the math.log() method. The math.log() will calculate the natural logarithms for these values and store them in the variables val1, val2, val3 respectively. Thus the code outputs 1.0 , 0.0 and 2.302585092994046

Method2: Use Python NumPy to Calculate the Natural Logarithm (ln)

To calculate the natural logarithm value of a number we can also use the numpy.log() method of the NumPy library of Python.

Syntax:

• Similar to the math.log method, with one argument, return the natural logarithm of x (to base e).
• With two arguments, return the logarithm of x to the given base, calculated as log(x)/log(base).

While using this method if no base value is provided, the value defaults to e, meaning that by only providing a number, you are automatically calculating the natural logarithm.

This may look like something happening not in the way we would expect it to but if we recall from the introduction that in many cases the base e is implicit, thus, many times it is omitted when referring to a log() function without a specified base.

Example

In this example, we will calculate and print the natural logarithm value for different values using the numpy.log() method.

Explanation of the example:

In the above example, we take the values e , 1 , and 10 and pass the values to the n.log() method (Here, NumPy is imported as n). The n.log() will calculate the natural logarithms for these values and store them in the variables val1, val2, val3 respectively. Thus the code outputs 1.0 , 0.0 and 2.302585092994046

Calculating the In of Elements of an Array in Python

So far, we have learned how to calculate the ln of a number using Python. But what if we have to calculate the ln of elements of an array?

We can use the numpy module to evaluate the ln of elements of an array in Python. The Numpy.log(arr, outArr) can be used to calculate the ln of elements of an Array in Python.

Syntax

Parameters

• arr: The arr parameter refers to the array whose ln we are supposed to evaluate.
• outArr: The outArr refers to the array where the log of the elements of the input array will be passed. This array needs to be of the same size as the input array.

Example

In this example, we will calculate the ln values of an array of numbers.

Explanation of the output:

In the above example, we are declaring a list temp and storing the numbers 10,20,30,40,50,60,70,80,90,100 . Now this list is converted into an array arr using the num.array() method of the numpy library. Now, the num.log(arr) will find the ln of arr and store it in res . Thus, the output is [2.30258509 2.99573227 3.40119738 3.68887945 3.91202301 4.09434456 4.24849524 4.38202663 4.49980967 4.60517019] .

How to Graph the Natural Log Function in Python

The natural log equation, being a function can be plotted on a graph. In this section, we will learn how to plot the natural log functions in Python.

In order to plot the graph for the natural log function in Python, we need to import the matplotlib library in our program.

We need to follow the following steps to plot the graph for the natural log function in Python:

• Step 1: We need to create an array of any size. In this case, we will create an array with numbers from 1 through 30.
• Step 2: We need to iterate through the array in order to create an array of the natural log.
• Step 3: Once we have got both arrays, we will plot the graph for the two arrays (the one with the original value and the one with logarithmic values) using the matplotlib library.

Plotting Natural Log (ln) vs Standard Log in Python

Similar to the natural log graph that we plotted in the previous section, we can also plot a standard log graph in Python. In this section, we will plot a Natural Log (ln) vs Standard Log graph in Python.

Again, in order to plot the graph for the natural log function in Python, we need to import the matplotlib library in our program.

We need to follow the following steps to plot the graph for the natural log function in Python:

• Step 1: We will make a list of integers.
• Step 2: We will convert the list to an array of integers using NumPy.
• Step 3: We will find the natural logarithm of the array and store it in another array.
• Step 4: We will find the standard logarithm of the array and store it in some other array. Now that we have got the logarithm arrays for both natural and standard logarithms, we will plot the graph.
• Step 5: We will use the graph.plot() method to plot the graph for the array (Here ‘graph’ is the alias used for ‘matplotlib.pyplot‘). We will pass the input array, the logarithmic array, and color, marker, and label parameters to set the color of the graph, line type of the graph, and the label of the graph respectively.
• Step 6: We will set the label for the axis using graph.xlabel and graph.ylabel .
• Step 7: We will set the title of the graph using graph.title() .
• Step 8: We will display the graph.

Conclusion

• The natural logarithm is defined as the given number’s logarithm to the base value.
• The base value in the case of natural logarithm is e.
• The Math.log() method of math library can be used to calculate ln in Python.
• The Numpy.log() method of numpy library can be used to calculate ln in Python.

See Also:

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How to Compute the Natural Logarithm (ln) in Python

Natural log python: In this tutorial we will see how to compute the natural logarithm using the math and numpy libraries.

Introduction

The natural logarithm (often abbreviated ln) is the inverse of the exponential function. It is often used in mathematics for calculations involving time and growth rates.

In python, several libraries allow us to compute it like the math library and the numpy library. In this tutorial we will see the following elements:

• Compute the natural logarithm using math
• Compute the natural logarithm using numpy
• Graphical representation using matplotlib
• Calculate the logarithm in base 2
• Calculate the logarithm in base 10

Let’s start with the math library.

Natural log python

Compute the natural log using math

The math library has a function called math.log(x) which returns the natural logarithm of x :

import math nlog1 = math.log(1) print(nlog1) nlog5 = math.log(5) print(nlog5) #Output: >>>0.0 >>>1.6094379124341003

Compute the natural log using numpy

The NumPy library also has a function called numpy.log() which allows the user to compute the natural logarithm of x where x belongs to all the elements of the input array.

import numpy as np input = [1, 100, 500, 20000] print("Input: ", input) output = np.log(input) print("Output: ", output) print("np.log(5) : ", np.log(5)) #Output: >>>Input: [1, 100, 500, 20000] >>>Output: [0. 4.60517019 6.2146081 9.90348755] >>>np.log(5) : 1.6094379124341003

Graphical representation using matplotlib

It is possible to graphically represent the results provided by the matplotlib library:

from matplotlib import pyplot as plt import numpy as np input = [1, 2, 3, 4, 5, 6, 7] output = np.log(input) plt.plot(input, input, color='blue', marker="*") # red for numpy.log() plt.plot(output, input, color='green', marker="o") plt.title("numpy.log() - Graphical representation using matplotlib") plt.xlabel("output") plt.ylabel("input") plt.show()

Here is the graphic representation:

Calculate the logarithm in base 2

If you want to use the logarithm in base 2, you can use the function numpy.log2(x) :

import numpy as np print(np.log2(1)) print(np.log2(5)) print(np.log2(10)) #Output: >>>0.0 >>>2.321928094887362 >>>3.321928094887362

Calculate the logarithm in base 10

If you want to use the logarithm in base 10, you can use the function numpy.log10(x) :

import numpy as np print(np.log10(1)) print(np.log10(5)) print(np.log10(10)) #Output: >>>0.0 >>>0.6989700043360189 >>>1.0

Conclusion

In this tutorial, we have seen how to calculate the natural logarithm in python using the NumPy and math libraries. These functions are widely used in mathematics and are quite easy to use.

If you don’t understand how to use them, don’t hesitate to tell me in the comments, I’m available to answer your questions.

See you soon for new tutorials !

I’m a data scientist. Passionate about new technologies and programming I created this website mainly for people who want to learn more about data science and programming 🙂

Источник

Python math.log() Method

The math.log() method returns the natural logarithm of a number, or the logarithm of number to base.

Syntax

Parameter Values

Parameter	Description
x	Required. Specifies the value to calculate the logarithm for. If the value is 0 or a negative number, it returns a ValueError. If the value is not a number, it returns a TypeError
base	Optional. The logarithmic base to use. Default is ‘e’

Technical Details

Return Value:	A float value, representing the natural logarithm of a number, or the logarithm of number to base
Python Version:	Changed in version 2.3
Change Log:	The base parameter was added

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