This calculator solves logarithmic equations (log₂(x) = 5), simplifies expressions (log(e²) = 2), expands logarithms using product/quotient/power rules, condenses multiple logs into one, and evaluates to decimal values. It supports natural log (ln), common log (log₁₀), binary log (log₂), and any custom base.
Solve finds the variable in a log equation. Expand breaks a single log into multiple logs using rules. Condense combines multiple logs into one. Simplify reduces to the simplest form. Evaluate computes a decimal result.
The calculator first attempts to solve using nerdamer (client-side CAS). It normalizes log bases, eliminates common denominators, and uses algebraic solving. If nerdamer cannot solve, it falls back to AI-powered step-by-step solutions. This gives instant results for standard problems and detailed explanations for complex ones.
ln (natural logarithm) is log base e (≈ 2.71828). log typically means log base 10 in everyday use. This calculator accepts both: type ln(x) or log(x) for natural log, and log10(x) for common log. Use log2(x) for binary log or logb(x, base) for any custom base.
Completely free with no signup. You get formula-based solving, AI step-by-step solutions, interactive Plotly graphs, a Python compiler, LaTeX export, shareable URLs, and a 2,000-problem practice worksheet. Most computation runs in your browser for instant results.
Yes. Click the Practice Worksheet button to open the worksheet engine with over 2,000 CAS-verified problems across 31 question types (solve equations, expand, condense, change of base, log derivatives/integrals, word problems, inequalities, and more) and 4 difficulty levels (basic, medium, hard, scholar). Each worksheet is randomly generated with a full answer key — perfect for exam prep, homework review, or classroom quizzes.
The worksheet covers 31 problem types: evaluate basic logs, solve single and multi-log equations, expand and condense (simple and complex), rewrite between log and exponential form, change of base, log inequalities, logarithmic differentiation, log derivatives and integrals, inverse properties, system of log equations, log limits, graphing log functions, domain of logs, and word problems. Problems range from basic textbook to scholar-level exam difficulty.
Yes. Click the 📷 Scan button and upload (or drop in) a photo of a handwritten or printed logarithm problem. The AI vision model extracts the expression (preserving log/ln subscripts and bases), fills the math field automatically, and detects whether to solve, expand, condense, or evaluate. Works on phone snapshots, textbook pages, whiteboard photos, and worksheet scans.