How this calculator works
Choose the structure inside the logarithm. Products split into addition, quotients split into subtraction, and powers become coefficients. The individual log terms are shown before they are combined. Arguments must be positive so each expanded term remains a real number. There is no corresponding rule that splits the logarithm of a sum.
Formula
log_n(ab) = log_n(a) + log_n(b); log_n(a/b) = log_n(a) - log_n(b); log_n(a^k) = k log_n(a).
Worked example
log_2(2 times 4) expands to 1 + 2 = 3. log_2(2^3) expands to 3 times 1 = 3.
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Frequently asked questions
Can I expand log(a + b)?
No. The product rule applies to multiplication inside the logarithm, not addition.
Why is log((-2)(-3)) rejected?
The product is positive, but the expanded real logarithms of -2 and -3 do not exist.
Does the power need to be an integer?
No. With a positive argument, a finite real exponent can move outside the logarithm.