Solve logarithms, inverse forms, base changes, and equations step by step. Check domains and rules. Graph outputs, save work, and compare example results quickly.
| Case | Expression | Result |
|---|---|---|
| Evaluate | log_2(32) | 5 |
| Evaluate | log_10(0.01) | -2 |
| Solve for x | log_3(x) = 4 | x = 81 |
| Solve for base | log_b(81) = 4 | b = 3 |
| Product rule | log_2(8 × 4) | log_2(8) + log_2(4) = 5 |
| Quotient rule | log_5(125 / 5) | log_5(125) - log_5(5) = 2 |
| Power rule | log_10(100^2) | 2 × log_10(100) = 4 |
Domain rules: the base must be positive, the base cannot equal 1, and every logarithm input must stay greater than 0.
A logarithm asks which exponent creates a number. In log_b(x) = y, the base b raised to y equals x. It reverses exponentiation.
A valid logarithm base must be greater than 0 and cannot equal 1. Negative bases and base 1 do not work in standard real logarithms.
Real logarithms are defined only for positive inputs. Zero and negative values fall outside the real-number domain for logarithmic evaluation.
Use natural logs for continuous growth and calculus work. Use common logs for powers of ten, scientific notation, and many school problems.
It converts any logarithm into a form using familiar logs. The rule is log_b(x) = ln(x) / ln(b), or the same idea with common logs.
Yes. It can evaluate a logarithm, solve for the input x, solve for the base, and expand expressions with product, quotient, or power rules.
The graph shows domain limits, slow growth, and where your solved point sits on the logarithmic curve. It also helps verify direction and scale.
The exports include the result summary and the step list. They are useful for assignments, revision notes, worksheets, and record keeping.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.