Simplify multiple log terms into one expression. Enter coefficients, powers, bases, and operations with ease. Review grouped arguments through clear symbolic output for practice.
| Example | Expanded Form | Condensed Form |
|---|---|---|
| 1 | log(x) + log(y) | log(xy) |
| 2 | 2log(a) - log(b) | log(a²/b) |
| 3 | 3ln(m) + 2ln(n) | ln(m³n²) |
| 4 | log₅(p) - 4log₅(q) | log₅(p/q⁴) |
The calculator uses three standard logarithm rules.
Product rule: log(A) + log(B) = log(AB)
Quotient rule: log(A) - log(B) = log(A/B)
Power rule: k·log(A) = log(Ak)
It first applies the power rule. Then it groups added terms in the numerator. Finally it places subtracted terms in the denominator.
Condensed logarithmic form makes long expressions shorter. It also reveals multiplication and division inside one log statement. This helps with algebra review. It also helps while solving exponential equations and simplifying symbolic work.
This calculator turns expanded log expressions into a single compact form. You can enter several terms. Each term may include a coefficient. Each argument may also include its own power. The calculator combines all terms using standard logarithm rules. It then shows the final condensed expression.
Each coefficient is applied first. This uses the power rule. For example, 3log(x) becomes log(x³). After that, added terms are multiplied together. Subtracted terms are moved into the denominator. This creates one final logarithm with one grouped argument.
This tool works well for homework checks. It is also useful for class practice. You can compare the entered form with the condensed result. The step list explains how each exponent was created. It also shows why a term belongs in the numerator or denominator.
Many learners use different log notations. Some use common logarithms. Others use natural logarithms. Some courses use custom bases. This page supports all three styles. That makes it easier to match textbook notation and teacher instructions.
The output is placed above the form after submission. This makes review faster. You do not need to scroll far. You can also export the result as CSV. The print button helps create a clean PDF copy for notes, assignments, or revision sheets.
It means rewriting several logarithmic terms as one logarithm. Addition becomes multiplication inside. Subtraction becomes division. Coefficients become exponents on arguments.
Yes. Select the natural log option. The calculator will return the result using ln notation instead of common log notation.
The calculator applies the power rule first. A coefficient becomes an exponent on that argument before terms are combined.
Yes. Choose the custom base option and enter the base value. The result will keep that base in the final expression.
Subtracted logarithmic terms represent division. Those arguments move below the fraction line in the final condensed form.
No. This page focuses on symbolic condensation. It rewrites the expression into one log statement instead of finding a decimal value.
Yes. Text arguments such as x+1, a-b, or 2y are accepted. Complex expressions are wrapped automatically when needed.
It saves time, reduces algebra mistakes, and shows the rule sequence clearly. That makes practice and checking much easier.
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.