np.exp() and np.log() in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of np.exp() on a numpy array

What is the output of the following code?

NumPy

import numpy as np
arr = np.array([0, 1, 2])
result = np.exp(arr)
print(result)

A [0 1 2]

B [1. 2.71828183 7.3890561 ]

C [1 1 1]

D [0. 1. 2.]

💡 Hint

Recall that np.exp(x) calculates e to the power of x for each element.

np.exp() calculates the exponential of each element. e^0=1, e^1≈2.718, e^2≈7.389.

❓ Predict Output

intermediate

Output of np.log() on a numpy array

What is the output of this code snippet?

NumPy

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

A [1. 1. 1.]

B [1. 2. 3.]

C [0. 1. 2.]

D [0. 0. 0.]

💡 Hint

np.log() returns the natural logarithm (base e) of each element.

Since log(e^x) = x, the output is [0, 1, 2].

❓ data_output

advanced

Result of combining np.exp() and np.log()

What is the output of this code?

NumPy

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

A [1. 2. 3.]

B [0. 0. 0.]

C [1 1 1]

D [2.71828183 7.3890561 20.08553692]

💡 Hint

Think about what happens when you apply exp to the log of a number.

np.exp(np.log(x)) returns x for positive x, so the output matches the original array.

🧠 Conceptual

advanced

Behavior of np.log() with zero and negative inputs

What happens when you run np.log() on an array containing zero or negative numbers?

NumPy

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

A It returns [-inf, nan, 0.] with a runtime warning.

B It returns [0, 0, 0] without any warnings.

C It raises a ValueError and stops execution.

D It returns [inf, -inf, 1] without warnings.

💡 Hint

Logarithm of zero or negative numbers is not defined in real numbers.

np.log(0) returns -inf, np.log(negative) returns nan, and a runtime warning is issued.

🚀 Application

expert

Calculate the geometric mean using np.log() and np.exp()

Given a numpy array of positive numbers, which code correctly calculates the geometric mean?

NumPy

import numpy as np
arr = np.array([1, 10, 100])

A np.mean(np.exp(arr))

B np.exp(np.sum(arr))

C np.log(np.mean(arr))

D np.exp(np.mean(np.log(arr)))

💡 Hint

Geometric mean is the nth root of the product of n numbers, which can be calculated using logs and exponentials.

Taking the log of numbers, averaging, then exponentiating gives the geometric mean.

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