This function is analogous to the builtin lambertw() except that it accepts the logarithm of the argument:
lambertw(0,exp(logx)) == lambertwlog(logx) (within machine precision)
This function only supports real values of logx and the principal branch of the Lambert W function (lambertw(0,x) for real, nonnegative x). For complex arguments or to evaluate alternative branches, use the builtin lambertw() function.

The logarithmic input allows for much larger arguments than the builtin lambertw(). For example,
lambertw(exp(710)) == Inf % exp(710) == Inf
lambertwlog(710) == 703.44
lambertwlog(10000) == 9990.79

Though limited in domain, this function is hundreds of times faster than the builtin version (as of MATLAB 8.5).