Lesson 63: Introduction to Logarithms
A logarithm is the inverse of an exponential function. If b^y = x, then log_b(x) = y. Here, b is the base (b > 0, b ≠1), x is the argument (x > 0), and y is the logarithm.
Key Points
- Definition: log_b(x) = y ⇔ b^y = x
- Common logarithm: log(x) has base 10
- Natural logarithm: ln(x) has base e (~2.718)
- Logarithms undo exponentials
Examples
Example 1: log_2(8) = 3 because 2^3 = 8
Example 2: log_5(25) = 2 because 5^2 = 25
Example 3: log_10(1000) = 3 because 10^3 = 1000
Example 4: ln(e^4) = 4 because e^4 = e^4
Practice Problems
- log_3(9) = ?
- log_4(64) = ?
- log_10(100) = ?
- ln(e^7) = ?
- Find x: 2^x = 16