Condense Logarithms Calculator

Combine a·log(x) + b·log(y) into a single logarithm value.

Base

Coefficient of log x

Coefficient of log y

Combined argument 45

Log value 1.653

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

Step-by-step with your numbers:

1. Values used:

2. Base = 10

3. Coefficient of log x = 2

4. x = 3

5. Coefficient of log y = 1

6. y = 5

8. Combined argument = 45

9. Log value = 1.653

Did we solve your problem today?

Condensing logarithms uses the power and product rules to merge several log terms into one.

The math behind it

Move coefficients into exponents (a·log x = log xᵃ), then combine sums into products: log xᵃ + log yᵇ = log(xᵃ·yᵇ).

2·log 3 + log 5 = log(9 × 5) = log 45.

What about subtraction?

A difference of logs condenses into a quotient: log x − log y = log(x/y).