Math

Condense Logarithms Calculator

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

Base

Coefficient of log x

Coefficient of log y

Calculated Output

Combined argument 45

Log value 1.653

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

Step-by-Step Breakdown

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

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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).