Condense a sum and difference of logarithms into a single logarithm: a·log(x) + c·log(y) − d·log(z) becomes one log of a single argument.
Result
How to use this tool
Enter the common logarithm base (not 1).
Enter each coefficient and argument: a·log(x), c·log(y) and d·log(z).
Read the single logarithm and its combined argument.
Read the numerical value of the condensed logarithm.
Formula & worked example
log₂(8) + log₂(4) − log₂(2) condenses to log₂(8 × 4 / 2) = log₂(16) = 4.
Limitations — read this before you rely on it
Single-expression condensing only: it does not parse free-text expressions, and all arguments must be positive.
Frequently asked questions
Combining several logs into one log of a single argument, using the product, quotient and power rules.
n·log(u) = log(u^n): a coefficient becomes an exponent inside the log.
log(u) + log(v) = log(u·v): adding logs multiplies their arguments.
log(u) − log(v) = log(u/v): subtracting logs divides their arguments.
Yes. The rules only combine logs that share the same base; convert bases first if they differ.