Condense Logarithms Calculator
MathCombine two logarithm terms with the same base into a single logarithm using the product rule.
Condensed Argument
The single argument of the condensed logarithm, a^x * b^y.
Condensed Value
3.547411
The numeric value of the condensed logarithm, log_n(a^x * b^y).
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Odeh Ahwal0people find this calculator helpful
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Saved
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Frequently Asked Questions
What is the product rule for condensing logarithms?
x*log_n(a) + y*log_n(b) = log_n(a^x * b^y). Coefficients in front of a logarithm can be moved inside as exponents, then two logs with the same base and a plus sign between them combine into the log of a product.
Why condense logarithms into one term?
A single logarithm is often easier to evaluate numerically, simplify further, or solve an equation with, compared to juggling multiple separate log terms.
Why is this limited to two terms?
Two terms cover the fundamental product-rule case and the large majority of textbook practice problems. More terms follow exactly the same rule applied repeatedly, combining one pair at a time.
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