Condense Logarithms Calculator
Combine x logₙ(a) + y logₙ(b) into one logarithm for numeric inputs.
Formula
x logₙ(a) + y logₙ(b) = logₙ(aˣbʸ)
Combined argument aˣbʸ ≈ (2)^(3)×(4)^(1) · Logarithm value ≈ ((3)×ln((2))+(1)×ln((4)))÷ln((2))
How to use
- Enter positive arguments a and b.
- Enter coefficients x, y and a positive base other than 1.
- Read the combined argument and the logarithm value.
Examples
- 3 log₂2 + log₂4 = log₂32 = 5.
Frequently asked questions
How do I enter subtraction?
Use a negative coefficient, such as y=−1.
Can the bases differ?
This identity requires a common base; convert bases first if necessary.
Does it simplify symbolic expressions?
No. It evaluates the displayed two-term identity from numbers you enter.
Sources
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