klist <- seq(1,100,by=2)

r1 <- 1/5
r2 <- 1/100

explist1 <- exp(-r1*klist)
explist2 <- exp(-r2*klist)

plot(klist, explist1+explist2, main = "sum of exponentials", xlab = "k", type = "h")

plot(klist, log(explist1+explist2), main = "log sum of exponentials", xlab = "k", type = "h")

par(mfrow = c(2,1))
plot(klist, explist1+explist2, xlab = "k", main = "split into two ranges",
     type = "h", xlim = c(0,15))
plot(klist, explist1+explist2, xlab = "k", main = "split into two ranges",
     type = "h", xlim = c(15,100))