Log Calculator

Simplify Logarithmic Calculations

This Logarithm Calculator allows you to find the log of a number to any base. It's a fundamental tool for students and professionals in science, engineering, and finance who work with exponential growth, pH levels, decibel scales, and more.

The Logarithm Explained

A logarithm answers the question: "What exponent do we need to raise a specific base to, in order to get a certain number?"

• For logₐ(b) = x, the equivalent exponential form is aˣ = b.
• Change of Base Formula: Most calculators only have buttons for base-10 (log) and base-e (ln). To calculate a logarithm to any other base, we use this formula: logₐ(b) = logₓ(b) / logₓ(a), where 'x' can be any base, usually 10 or e.

How to Use the Calculator

1. Number: Enter the number you want to find the logarithm of.
2. Base: Enter the base of the logarithm.
3. Calculate: The tool will display the result.

Real-World Example

You want to calculate log₂(8). This is asking, "To what power must we raise 2 to get 8?"

1. Number: 8
2. Base: 2

• The calculator will show the result: 3, because 2³ = 8.

Another example: log₁₀(100)

1. Number: 100
2. Base: 10

• The result is 2, because 10² = 100.

Frequently Asked Questions (FAQ)

• What's the difference between 'log' and 'ln'?
  • log usually implies a base of 10 (the common logarithm).
  • ln implies a base of e (Euler's number, ≈ 2.718), which is the natural logarithm.
• Why can't I take the log of a negative number or zero? There is no exponent you can raise a positive base to that will result in a negative number or zero. Therefore, the logarithm is only defined for positive numbers.
• Why can't the base be 1? One raised to any power is always one. It's impossible to get any other number, so base 1 logarithms are undefined.