[Rafael-SOWNet]

An equation in two or more logarithms of x had no route of its own. It came to Newton's method, which answered in decimals and left out any root it didn't reach.

k_1 log_b(P_1) + … + k_n log_b(P_n) = c, for polynomials P_i, rational k_i and one base, holds only where P_1^(k_1 L) … P_n^(k_n L) = b^(c L), with L the common denominator of the k_i. That is a polynomial equation, and its roots are found exactly. Each one is put back into the equation as written, under the principal logarithm, and kept only where it holds, since over the complex numbers ln(u) + ln(v) is ln(u v) only up to 2 pi i. Over the reals each argument must also be positive.

Solve("x")	2.6.0 and master	now
ln(x) + ln(x + 1) = 0	{ 0.6180339887498947… }	{ (-1 + sqrt(5)) / 2 }
ln(1 + 3x^2) - ln(4x) = 1	{ 3.529945609977906… }	both roots, (4e ± sqrt(16e^2 - 12)) / 6
ln(-1 - 3x^2) - ln(4x) = 1	{ -3.529945609977908… }, and on master … - 1.3E-15i	both roots, negated, whose i pi cancel
ln(x^2 + 1) - ln(x) = 1	two decimals	(e ± sqrt(e^2 - 4)) / 2
ln(x) + ln(x - 1) = ln(6)	{ 3 }	{ 3 }; at -2 the sum is ln(6) + 2 pi i

• Measured on 400 random equations of this kind against a Newton search under the principal logarithm. Master answers 292, leaves 108 unsolved and misses 25 roots across 22 of its answers. This answers all 400, none unsound and none missing a root. The slowest takes 251 ms.
• It declines where it can't be sure, leaving the equation to the routes after: a residual too small to tell from rounding, or a candidate that isn't a root of the polynomial it solved. 3x^3 + 9x^2 + 9x + 1 is one, since the polynomial solver answers it with a non-root until A cube shifted is solved #2315.
• Six of the ten new cases fail on master. The other four have rational roots, which Newton's search plus rounding lands on exactly. The suite, the trio, F#, AOT and the eight harnesses pass. BREAKING-CHANGES.md has an entry.

No issue was filed.

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Codecov Report

❌ Patch coverage is 71.79487% with 22 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.75%. Comparing base (9880e18) to head (095f734).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
...ntinuous/Solvers/EquationSolver/LogarithmSolver.cs	71.05%	11 Missing and 11 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2316      +/-   ##
==========================================
- Coverage   86.78%   86.75%   -0.03%     
==========================================
  Files         311      312       +1     
  Lines       68221    68299      +78     
  Branches    19828    19857      +29     
==========================================
+ Hits        59203    59255      +52     
- Misses       4877     4890      +13     
- Partials     4141     4154      +13     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.30% <71.79%> (-0.03%)	⬇️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

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Files with missing lines	Coverage Δ
...Solvers/EquationSolver/AnalyticalEquationSolver.cs	96.45% <100.00%> (+0.05%)	⬆️
...ntinuous/Solvers/EquationSolver/LogarithmSolver.cs	71.05% <71.05%> (ø)

... and 6 files with indirect coverage changes

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