np.exp() and np.log() in NumPy - Mini Project: Build & Apply

Using np.exp() and np.log() for Data Transformation

📖 Scenario: Imagine you are analyzing daily growth rates of a small plant species. You have recorded the growth rates as percentages, and you want to understand the exponential growth and also convert back from exponential values to the original growth rates.

🎯 Goal: You will create a numpy array of growth rates, apply the exponential function to simulate growth, then use the natural logarithm to retrieve the original rates. This helps understand how exponential and logarithmic functions work in data science.

📋 What You'll Learn

Create a numpy array with exact growth rates

Create a variable to hold the base of natural logarithm (e)

Use np.exp() to calculate exponential growth

Use np.log() to convert exponential values back to original growth rates

Print the final results

💡 Why This Matters

🌍 Real World

Exponential and logarithmic functions are used in biology to model growth, in finance to calculate compound interest, and in many data science tasks to transform data for analysis.

💼 Career

Understanding how to apply np.exp() and np.log() is important for data scientists working with growth models, time series data, and feature engineering.

1

Create the growth rates array

Import numpy as np and create a numpy array called growth_rates with these exact values: 0.05, 0.10, 0.15, 0.20, 0.25.

NumPy

import numpy as np
# Create the growth_rates array with the exact values
# Your code here

Hint

Use np.array() to create the array with the given values.

2

Create the constant for natural logarithm base

Create a variable called e and assign it the value of the mathematical constant e using np.e.

NumPy

import numpy as np
growth_rates = np.array([0.05, 0.10, 0.15, 0.20, 0.25])
# Create the variable e using np.e
# Your code here

Hint

Use np.e to get the value of e.

3

Calculate exponential growth and apply logarithm

Create a variable called exp_growth by applying np.exp() to growth_rates. Then create a variable called log_values by applying np.log() to exp_growth.

NumPy

import numpy as np
growth_rates = np.array([0.05, 0.10, 0.15, 0.20, 0.25])
e = np.e
# Calculate exp_growth using np.exp on growth_rates
# Calculate log_values using np.log on exp_growth
# Your code here

Hint

Use np.exp() to get exponential values and np.log() to get back the original values.

4

Print the exponential and logarithmic results

Print the variables exp_growth and log_values each on a separate line.

NumPy

import numpy as np
growth_rates = np.array([0.05, 0.10, 0.15, 0.20, 0.25])
e = np.e
exp_growth = np.exp(growth_rates)
log_values = np.log(exp_growth)
# Print exp_growth
# Print log_values
# Your code here

Hint

Use two print() statements to display the arrays.

Practice

1. What does the function np.exp(x) compute in NumPy?

easy

A. The square root of x

B. The value of e raised to the power x

C. The natural logarithm of x

D. The sine of x

Solution

1. Step 1: Understand the purpose of np.exp()

   The function np.exp() calculates e (Euler's number, approximately 2.718) raised to the power of the input value.

2. Step 2: Compare with other options

   Other options describe different functions: natural log is np.log(), square root is np.sqrt(), sine is np.sin().

3. Final Answer:

   The value of e raised to the power x -> Option B

4. Quick Check:

   np.exp(x) = e^x [OK]

Hint: Remember: exp means e to the power x [OK]

Common Mistakes:

• Confusing np.exp() with np.log()
• Thinking np.exp() calculates logarithm
• Mixing up with square root or trigonometric functions

2. Which of the following is the correct syntax to compute the natural logarithm of a NumPy array arr?

easy

A. np.log(arr)

B. np.exp(arr)

C. np.ln(arr)

D. np.log10(arr)

Solution

1. Step 1: Identify the function for natural logarithm

   The natural logarithm in NumPy is computed using np.log().

2. Step 2: Check other options for correctness

   np.exp() calculates exponentials, np.ln() does not exist, and np.log10() calculates base-10 logarithm.

3. Final Answer:

   np.log(arr) -> Option A

4. Quick Check:

   Natural log = np.log() [OK]

Hint: Natural log uses np.log(), not np.ln() or np.log10() [OK]

Common Mistakes:

• Using np.ln() which is not a valid NumPy function
• Confusing natural log with base-10 log
• Using np.exp() instead of np.log()

3. What is the output of the following code?

import numpy as np
arr = np.array([1, 2, 3])
result = np.log(np.exp(arr))
print(result)

medium

A. [1. 2. 3.]

B. [0. 0. 0.]

C. [2.718 7.389 20.086]

D. Error: invalid input

Solution

1. Step 1: Understand the inner function np.exp(arr)

   Applying np.exp() to [1, 2, 3] gives [e^1, e^2, e^3] ≈ [2.718, 7.389, 20.086].

2. Step 2: Apply np.log() to the result

   Taking the natural log of these values returns the original array [1, 2, 3] because log and exp are inverse functions.

3. Final Answer:

   [1. 2. 3.] -> Option A

4. Quick Check:

   np.log(np.exp(x)) = x [OK]

Hint: log(exp(x)) returns x because they undo each other [OK]

Common Mistakes:

• Expecting the exponential values instead of original
• Confusing output with zeros
• Thinking it causes an error

4. Identify the error in the following code snippet:

import numpy as np
arr = np.array([-1, 0, 1])
result = np.log(arr)
print(result)

medium

A. np.log() should be np.exp()

B. np.array() syntax is incorrect

C. np.log() cannot take zero or negative values

D. No error, code runs fine

Solution

1. Step 1: Check input values for np.log()

   Natural logarithm is undefined for zero and negative numbers. The array contains -1 and 0, which cause errors or warnings.

2. Step 2: Understand the error behavior

   NumPy will return -inf or NaN for zero or negative inputs, which is usually an error or warning in calculations.

3. Final Answer:

   np.log() cannot take zero or negative values -> Option C

4. Quick Check:

   Log input must be positive [OK]

Hint: Logarithm inputs must be positive numbers only [OK]

Common Mistakes:

• Ignoring domain restrictions of log function
• Confusing np.log() with np.exp()
• Assuming code runs without warnings or errors

5. You have a dataset of positive values stored in a NumPy array data. You want to normalize it by applying the natural logarithm, then reverse the transformation after some processing. Which sequence of operations correctly achieves this?

hard

A. Apply np.exp(data) first, then np.log() on the result to reverse

B. Apply np.sqrt(data) first, then np.log() on the result to reverse

C. Apply np.log10(data) first, then np.exp() on the result to reverse

D. Apply np.log(data) first, then np.exp() on the result to reverse

Solution

1. Step 1: Understand the normalization step

   Applying np.log(data) transforms data to a logarithmic scale, useful for normalization.

2. Step 2: Reverse transformation

   To get back original data, apply np.exp() to the logged data because exp is the inverse of log.

3. Step 3: Check other options

   Apply np.exp(data) first, then np.log() on the result to reverse reverses the order incorrectly, Apply np.log10(data) first, then np.exp() on the result to reverse mixes log base 10 with exp (base e), Apply np.sqrt(data) first, then np.log() on the result to reverse uses sqrt which is unrelated.

4. Final Answer:

   Apply np.log(data) first, then np.exp() on the result to reverse -> Option D

5. Quick Check:

   log then exp returns original data [OK]

Hint: Log then exp reverses; order matters [OK]

Common Mistakes:

• Reversing the order of log and exp
• Mixing log base 10 with exp
• Using unrelated functions like sqrt