Logarithm Calculator

Compute Logarithms to Any Base with Step-by-Step Solutions

Calculate \( \log_b(x) \) and see the equivalent exponential form \( b^y = x \).

Logarithm Definition

The logarithmic function \( \log_b(x) \) is the inverse of the exponential function \( b^x \):

\[ y = \log_b(x) \quad \iff \quad x = b^y \]

where \( x > 0 \), \( b > 0 \), and \( b \neq 1 \).

\( x \) (argument)

\( b \) (base)

Decimal places:

Enter argument \( x > 0 \). Base \( b > 0, b \neq 1 \). Use "e" for natural logarithm.

Result will appear here

Enter x and base, then click "Calculate Logarithm"

📐 Step-by-step solution will appear here after calculation.

Logarithm Rules

Product Rule: \( \log_b(x \cdot y) = \log_b(x) + \log_b(y) \)

Quotient Rule: \( \log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y) \)

Change of Base Formula: \( \log_b(x) = \frac{\log_B(x)}{\log_B(b)} \) for any base \( B \)