np.exp() and np.log() in NumPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the exponential of each element in the array.

NumPy

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

Drag options to blanks, or click blank then click option'

Aexp

Blog

Csqrt

Dsin

Attempts:

3 left

💡 Hint

Common Mistakes

Using np.log() instead of np.exp()

Using math.exp() which does not work element-wise on arrays

The np.exp() function calculates the exponential (e^x) of each element in the array.

2fill in blank

medium

Complete the code to calculate the natural logarithm of each element in the array.

NumPy

import numpy as np
arr = np.array([1, np.e, np.e**2])
result = np.[1](arr)
print(result)

Drag options to blanks, or click blank then click option'

Aexp

Blog10

Csqrt

Dlog

Attempts:

3 left

💡 Hint

Common Mistakes

Using np.exp() instead of np.log()

Using np.log10() which calculates log base 10

The np.log() function calculates the natural logarithm (log base e) of each element in the array.

3fill in blank

hard

Fix the error in the code to correctly compute the exponential of the array elements.

NumPy

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

Drag options to blanks, or click blank then click option'

Aexp

Bsqrt

Carray

Dlog

Attempts:

3 left

💡 Hint

Common Mistakes

Using np.log() which calculates logarithm

Trying to call np.array() as a function on the list

The input arr is a list, but np.exp() can handle lists by converting them internally. The function to compute exponential is exp.

4fill in blank

hard

Fill both blanks to create a dictionary with words as keys and their lengths as values, but only include words longer than 3 characters.

NumPy

words = ['data', 'is', 'fun', 'and', 'easy']
lengths = {word: [1] for word in words if [2]
print(lengths)

Drag options to blanks, or click blank then click option'

Alen(word)

Bword > 3

Clen(word) > 3

Dword

Attempts:

3 left

💡 Hint

Common Mistakes

Using the word itself instead of its length

Comparing the word string directly to a number

The dictionary comprehension uses len(word) to get the length, and the condition len(word) > 3 to filter words longer than 3 characters.

5fill in blank

hard

Fill all three blanks to create a dictionary with uppercase words as keys and their logarithm values as values, but only include words with length greater than 2.

NumPy

import numpy as np
words = ['hi', 'log', 'data', 'np']
result = { [1]: np.[2](len(word)) for word in words if len(word) [3] 2 }
print(result)

Drag options to blanks, or click blank then click option'

Aword.upper()

Blog

C>

Dexp

Attempts:

3 left

💡 Hint

Common Mistakes

Using np.exp instead of np.log

Not converting words to uppercase

Using wrong comparison operator

The dictionary keys are uppercase words using word.upper(). The values are the natural logarithm of the word length using np.log. The filter keeps words with length greater than 2.

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