How this calculator works
Use the power rule to move each coefficient inside its logarithm. A sum multiplies those powered arguments, while a difference divides them. All original arguments must be positive even if a combined expression could otherwise look valid. The recovery modes solve a weighted sum; their labels identify that assumption.
Formula
x log_n(a) + y log_n(b) = log_n(a^x b^y); replace + with - to divide. x log_n(a) = log_n(a^x).
Worked example
log_2(2) + log_2(4) condenses to log_2(8), which equals 3. log_10(100) - log_10(10) becomes log_10(10) = 1.
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Frequently asked questions
Must all logs have the same base?
Yes. Convert bases first when the original terms use different bases.
What do the coefficients do?
Each coefficient becomes an exponent on its argument. For example, 3 log_2(2) becomes log_2(2^3).
Can I condense logs of negative numbers?
This real-number tool requires every original argument to be positive.