📊 NumPy Logarithmic Functions

NumPy provides a set of vectorized logarithmic functions to perform element-wise logarithmic calculations on arrays. These functions are much faster than using Python’s math library with loops.

✅ 1. Natural Logarithm (np.log)

• Computes the natural logarithm (base e) of each element.

• np.e ≈ 2.71828

✅ 2. Base-2 Logarithm (np.log2)

• Computes the logarithm base 2 of each element.

• Useful in binary computations

✅ 3. Base-10 Logarithm (np.log10)

• Computes the logarithm base 10 of each element.

• Commonly used in scientific notation and pH calculations

✅ 4. Logarithm of 1 Plus (np.log1p)

• Computes log(1 + x) accurately for small x

• Avoids loss of precision for tiny numbers

• Useful in data normalization and machine learning

✅ 5. Applying Logs to 2D Arrays

• Operations are element-wise on all dimensions

✅ 6. Notes & Tips

• Logarithms cannot be applied to zero or negative numbers → returns -inf or NaN.

• Always ensure input array has positive values.

• Use np.log1p for small values near zero to avoid precision errors.

🎯 Practice Exercises

1. Create an array [1, 2, 4, 8, 16] and compute log, log2, log10.

2. Generate 1D array of small numbers [1e-10, 1e-5, 0.1] and use np.log1p.

3. Create a 2×3 array and compute log10 of all elements.