Interactive Math Tool

Logarithm & Exponent Explorer

Compute, visualize, and master log/exponent rules with step-by-step solutions, interactive graphs, and practice challenges.

📐 Logarithm Calculator

Base (b)

Argument (x)

⚡ Exponent Calculator

Base (b)

Exponent (n) — supports fractions like 2/3

📈 Interactive Graph

Base b: e

▬ y = b^x (exponential) ▬ y = log_b(x) (logarithm) - - - y = x (mirror line)

📖 Rules Explorer

Exponent Rules

Product Rule

\( b^m \times b^n = b^{m+n} \)

Quotient Rule

\( b^m \div b^n = b^{m-n} \)

Power of a Power

\( (b^m)^n = b^{mn} \)

Power of a Product

\( (ab)^n = a^n \times b^n \)

Zero Exponent

\( b^0 = 1 \)

Negative Exponent

\( b^{-n} = \frac{1}{b^n} \)

Fractional Exponent

\( b^{m/n} = \sqrt[n]{b^m} \)

Logarithm Rules

Product Rule

\( \log_b(xy) = \log_b(x) + \log_b(y) \)

Quotient Rule

\( \log_b\!\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y) \)

Power Rule

\( \log_b(x^n) = n \cdot \log_b(x) \)

Change of Base

\( \log_b(x) = \frac{\log_c(x)}{\log_c(b)} \)

Identity Rules

\( \log_b(b) = 1 \quad\text{and}\quad \log_b(1) = 0 \quad\text{and}\quad b^{\log_b(x)} = x \)

🧮 Equation Solver

Solve b^x = n for x.

Base (b)

Result (n)

Solve log_b(x) = n for x.

Base (b)

A = P(1 + r/n)^nt — leave one field blank to solve for it.

Principal (P)

Rate (r, decimal)

Compounds/yr (n)

Time in years (t)

Final Amount (A)

y = y₀ e^kt — leave one field blank to solve for it.

Initial (y₀)

Rate constant (k)

Time (t)

Final (y)

🎯 Practice Mode

Score

Streak

Attempted

Press "New Question" to start!