Expanding Logarithms Calculator

Your details

Choose which log property to expand. Product and quotient rules take two arguments; the power rule takes a base argument and an exponent.
Select a standard base or choose "Custom base" to enter any positive base other than 1.
The first factor (product/quotient rules) or the base argument (power rule). Must be positive.
The second factor (product rule) or divisor (quotient rule). Must be positive.
Expanded expression
log(8) + log(4)

The logarithm written out using the selected property

log(a) value0.90309
log(b) or k-log(a) value0.60206
Combined numerical result1.50515
log(a)0.90309
log(b) / k*log(a)0.60206
Combined result1.50515

Expanded using the product rule: log(8) + log(4)

  • The product rule splits one logarithm of a product into a sum of two separate logarithms, making many expressions easier to work with algebraically.
  • log(a) evaluates to 0.9031 and log(b) evaluates to 0.6021, summing to 1.5051.
  • This rule is the foundation for logarithm-based proofs and simplifications in algebra and calculus.

Next stepIf your expression combines product, quotient, and power terms together, apply each rule in turn - products and quotients first, then bring down exponents with the power rule.

 = Powered by OnlyCalculators