np.exp() and np.log() in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does the function np.exp() do in numpy?

np.exp() calculates the exponential of all elements in the input array. It raises the mathematical constant e (about 2.718) to the power of each element.

beginner

What is the purpose of np.log() in numpy?

np.log() computes the natural logarithm (log base e) of each element in the input array. It is the inverse operation of np.exp().

beginner

If x = np.array([1, 2, 3]), what is the output of np.exp(x)?

The output is an array where each element is e raised to the power of the corresponding element in x:

[e^1, e^2, e^3] ≈ [2.718, 7.389, 20.086]

intermediate

What happens if you apply np.log() to an array containing zero or negative numbers?

Applying np.log() to zero or negative numbers results in -inf or nan values and usually raises a warning, because the natural logarithm is not defined for those values.

intermediate

How are np.exp() and np.log() related mathematically?

np.exp() and np.log() are inverse functions. This means np.exp(np.log(x)) = x for positive x, and np.log(np.exp(x)) = x for any real x.

What does np.exp(0) return?

A 0

B e

C 1

D Undefined

Since e^0 = 1, np.exp(0) returns 1.

Which numpy function would you use to find the natural logarithm of an array?

A np.log()

B np.power()

C np.sqrt()

D np.exp()

np.log() calculates the natural logarithm of each element.

What is the result of np.log(np.exp(3))?

A 0

B e^3

C Undefined

D 3

Because np.log() and np.exp() are inverse functions, the result is 3.

What will np.log(-1) return?

A nan or warning

B A real number

C 0

D 1

Natural logarithm of negative numbers is not defined in real numbers, so numpy returns nan and raises a warning.

If arr = np.array([1, 2, 3]), what does np.exp(arr) compute?

A Natural logarithm of each element

B e raised to the power of each element

C Square of each element

D Sum of elements

np.exp(arr) calculates e to the power of each element in the array.

Explain in your own words what np.exp() and np.log() do and how they are related.

Think about how one function can undo the effect of the other.

Describe what happens if you try to take the natural logarithm of zero or a negative number using np.log().

Consider the domain of the logarithm function.

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