Expanding Logarithms Calculator

Expand log(xᵃ · yᵇ) into separate logarithm terms.

Base

Exponent on x

Exponent on y

a·log x 0.9542

b·log y 0.699

Sum (= log of product) 1.653

Formula: log(xᵃ·yᵇ) = a·log x + b·log y

Step-by-step with your numbers:

1. Values used:

2. Base = 10

3. x = 3

4. Exponent on x = 2

5. y = 5

6. Exponent on y = 1

8. a·log x = 0.9542

9. b·log y = 0.699

10. Sum (= log of product) = 1.653

Did we solve your problem today?

Expanding logarithms breaks one log of a product/power into a sum of simpler logs.

The math behind it

log(xᵃ·yᵇ) = a·log x + b·log y, using the product and power rules in reverse of condensing.

log(3²·5) = 2·log 3 + log 5.

Can I expand a quotient?

Yes — log(x/y) = log x − log y.