Logarithm

In reality complexities are not simple.

Logarithm complexities appears more often that we migh want to accept.

Logarithm of a number rougly measures the number of times we can divide that number by the base before you get a number less that that number or equal to that number.

complexity

Algorithm with (log n) time complexity is great.
Recursion contains logarithm space complexities

Who cares

certain algorithm contain log complexities
Efficient sorting algorithm involves logarithm

🧠 Common Logarithms in Programming

Base 10 → Math.log10(x)
Base 2 → Math.log2(x)
Natural log (base e ≈ 2.718) → Math.log(x)

console.log(Math.log2(8));    // 3
console.log(Math.log10(100)); // 2
console.log(Math.log(1));     // 0 (natural log)
 
 
🚩 What is a Logarithm?
A logarithm answers the question:
 
To what power must a certain number (the base) be raised to produce another number?
 
 
Where:
- `b` = base
- `x` = result
- `y` = exponent
 
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## ✅ Examples
 
| Expression        | Meaning     | Explanation                    |
|------------------|-------------|--------------------------------|
| `log₁₀(1000) = 3` | `10^3 = 1000` | Base 10 raised to 3 is 1000    |
| `log₂(8) = 3`     | `2^3 = 8`     | Base 2 raised to 3 is 8        |
| `log₁₀(1) = 0`    | `10^0 = 1`    | Any base raised to 0 is 1      |

Last updated on May 28th, 2025