Logarithm (Log) Calculator

• Choose the base using the quick toggle (10, e, 2, or custom).
• Enter the argument x (must be > 0).
• Click Calculate to get the value, steps, and the curve visual.

• Definition: If b^y = x, then y = log_b(x).
• Change of base: log_b(x) = ln(x)/ln(b) (works for any valid base).
• Domain: x > 0, b > 0, and b ≠ 1.

Example 1 — log₁₀(1000)

1. Base b = 10, argument x = 1000.
2. Because 10³ = 1000, we get log₁₀(1000) = 3.

Example 2 — log₂(1/8)

1. x = 1/8 = 2^-3.
2. So log₂(1/8) = -3.

Example 3 — Change of base

1. To compute log₃(10), use ln(10)/ln(3).
2. This gives a decimal approximation.