Evaluate real logarithms and recover arguments or bases, with natural, common and binary modes and explicit numerical domain limits.
01 / PURPOSE-SPECIFIC INPUTS
02 / RESULT & SUPPORTING WORK
Real-number floating-point evaluation only; displayed precision does not make a rounded decimal mathematically exact. Complex logarithms and unrepresentable overflow/underflow are not modeled.
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Real logarithm and exponential relationships are solved with explicit argument/base domains. The calculator explains inverse ambiguity, numerical precision and equivalent exponential forms rather than pretending to provide complex arithmetic.
Choose seven logarithm/inverse modes with stable near-one evaluation, configurable display precision and clear real-domain errors.
Log Calculator inputs and calculations remain in browser memory. No external processing API receives entered measurements, formulas, dates or financial values. Ordinary website page requests may still be logged. Clipboard access occurs only when you choose Copy Result.
Custom-base, natural, common and binary logarithms are supported, plus argument recovery, base recovery and antilogarithm. All modes use real numbers; complex logarithms are not modeled.
A real logarithm needs a positive argument and a positive base other than one. Bases between zero and one are valid. The literal e is accepted as the natural-base constant; NaN, infinity and unrepresentable results are rejected.
For any valid base, log_b(1) = 0. When recovering a base from x = 1 and y = 0, infinitely many valid bases exist; a unique base is not invented. With y nonzero, the recovered base would be one and is invalid.
Argument recovery and antilogarithm use x = b^y. Base recovery uses b = exp(ln(x)/y), with checks for zero y, nonpositive values, invalid base one and numeric overflow or underflow.
For values near one, the implementation uses log1p(value−1). This reduces avoidable numerical cancellation, but cannot restore digits that were already lost when an entered decimal rounds to machine-precision one.
No. It changes displayed decimal places or scientific-mantissa places only. The equivalent exponential form and other logarithm values are finite floating-point evaluations, not claims of exact symbolic mathematics.