Facing a simple, yet frustrating formula like this
Using the results from Wolfram Alpha I was able to find the solution with the ‘gsl’ library
# install.packages("gsl") library(gsl) # create some example data dat <- data.frame(a = 0.109861, x = 10) # a is set so that b is roughly 30. # Lazy as I am I used Excel and its solver ability to find numbers # to check if b is close to 30. Using the initial formula dat$b <- dat$x * exp(dat$a * dat$x) dat # solve for x2 and see if x and x2 are similar and close to 10 dat$x2 <- lambert_W0(dat$a * dat$b)/dat$a dat # a x b2 x2 #1 0.109861 10 29.99993 10.00001 # Hurray!
Sometimes life can be so easy (after a long time searching for the right results….).