I usually suggest the techniques in gosper.org/newsrope.pdf , but everything I've tried for 50^x - 49^x = 2 converges abysmally. —rwg On 2018-10-19 12:41, Henry Baker wrote:

I can solve this equation with Newton's iterations, but I was curious if there might be an elegant closed form solution.

I tried fiddling with hyperbolic trig functions, but nothing seemed any simpler.

real a>b>0,c>0

E.g., a ~ 50, b ~ 49, c ~ 2 => x ~ 1.1438929