Log Calculator
Calculate common logarithms, natural logarithms, and log expressions with fractions, exponents, constants, and roots.
Log calculator for log, ln, powers, and fractions
Use this log calculator for common logarithms, natural logarithms, and expressions where logs appear inside fractions or powers.
The calculator recognizes log as base 10 and ln as the natural logarithm.
Features
- log and ln function buttons.
- Common logarithm and natural logarithm support.
- Log expressions with fractions and exponents.
- Readable 2D input for complex formulas.
- Errors for log(0) and negative real logarithms.
Example expressions
\log(100)\log(1000)\ln(e^2)\frac{\log(1000)}{3}\ln(\sqrt{e})\frac{\log(100)}{\ln(e^2)}
How to use this calculator
- Use log(x) for base-10 logarithms and ln(x) for natural logarithms.
- Place the full argument inside parentheses or the function template.
- Combine logs with fractions or powers after confirming the argument is positive.
Common input mistakes
- log(0) and log of a negative real number are undefined in this calculator.
- Do not confuse log with ln: log is base 10, ln is base e.
- If a log is inside a fraction, keep the whole log expression in the numerator or denominator.
FAQ
What is log in this calculator?
log is interpreted as the common logarithm, base 10.
What is ln?
ln is the natural logarithm, base e.
Can I divide logarithms in a fraction?
Yes. Use a fraction structure and put log or ln expressions in the numerator and denominator.
Why does log(0) show an error?
The real logarithm is only defined for positive inputs, so zero and negative inputs are rejected.