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Two and only two (Posted on 2015-11-03)

For what value(s) of n does the equality sin(x) = log_n(x) have exactly two solutions?

See The Solution Submitted by broll

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re: a quick look

| Comment 3 of 4 |

(In reply to a quick look by Charlie)

A closer approximation for the first value given is 7.8229

 x      sin(x)          log(7.8229)(x)       difference
7.75 .994598779111176 .995448597662659    -8.49818551483173E-04
7.76 .995586975859855 .996075460154489    -4.88484294634634E-04
7.77 .996475614740601 .996701515353769    -2.25900613168895E-04
7.78 .997264606890266 .997326765337137    -6.21584468710895E-05
7.79 .997953873410293 .997951212173227     2.66123706624949E-06
7.8 .998543345374605 .998574857922713    -3.15125481084478E-05
7.81 .999032963836496 .999197704638349    -1.64740801853564E-04
7.82 .999422679834528 .999819754365008    -3.97074530480379E-04
7.83 .999712454397426 1.00044100913972    -7.28554742297353E-04
7.84 .999902258547975 1.00106147099173    -1.15921244375285E-03
7.85 .999992073305919 1.0016811419425    -1.6890686365775E-03

Posted by Charlie on 2015-11-03 14:58:18

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