[math-fun] a^x-b^x=c, solve for x ?

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