Concepts Simplified: What Is a Logarithm?

What is a Logarithm?

A logarithm answers the question:
"To what power must I raise a number (called the base) to get another number?"

Example

$$ \log_2 8 = ? $$ To what power must I raise 2 to get 8?
Since $2^3 = 8$, we say: $$ \log_2 8 = 3 $$

General Form

$$ \log_b x = y \quad \text{means} \quad b^y = x $$

Real-Life Analogy

Logarithms are like the opposite of exponents. If: $$ 10^2 = 100, \quad \text{then} \quad \log_{10} 100 = 2 $$

Why It's Useful

• Used in sound (decibels), earthquakes (Richter scale), and pH levels
• Helps solve equations involving exponents
• Common in computer science (binary logarithms)