Mode
Choose a mode, enter the base and expression, then compute to see symbolic steps and shareable outputs.
Results
How it’s calculated
FAQ
Which log transformations does this calculator cover?
It handles the product, quotient, and power rules for expansion, condenses signed sums into one log, converts between bases (showing both log10 and ln forms), and evaluates numeric values.
What domain checks are enforced?
Before computing, the tool requires a>0, b>0, and b≠1 for numeric modes. Any input outside this domain raises an error instead of a misleading result.
Which transformation should I try first?
Choose expand when one logarithm contains products, quotients, or powers. Choose condense when several logarithm terms should become one expression, and choose change of base when you need a numeric evaluation.
Why does the calculator reject some logarithms?
Logarithm arguments must be positive, and a numeric base must be positive and not equal to 1. The tool blocks invalid domains instead of simplifying them into a misleading expression.
How should I check the displayed steps?
Compare each line with the product, quotient, power, or change-of-base rule named in the output. If a sign changes, check whether it came from a quotient or a negative coefficient.
How to use the log laws transformer effectively
Choose the algebra direction
Expansion breaks one logarithm into several terms. Condensing combines terms into one logarithm. Change of base rewrites the expression so it can be evaluated with common calculator functions.
Check domains before simplifying
Every logarithm argument must stay positive, and numeric bases must be positive and not equal to 1. A formally simplified expression is only valid where those domain rules hold.
Use-case sequence
Start with the rule you want to demonstrate, run the transformation, then compare each displayed step with the matching product, quotient, power, or base-change identity.
Common mistakes to avoid
Do not distribute logarithms over sums, drop coefficients during condensing, or ignore a negative sign before a logarithm. These are the most common sources of wrong transformations.
Interpretation guidance
Use the final expression together with the steps. The steps explain the algebra rule, while the final line gives the compact form or numeric value.