Fitting a log curve based on size of a text to detect the knee point

Question

I am producing a plot based on the width of a text column to determine the "knee point" based on the curve that is generated. I want more granular numbers so that I can be more specific in the size of the text.

I have tried the following:

library(textshaping)
library(dplyr)

df%>% 
  mutate(width_txt = text_width(title)) %>% 
  pull(width_txt) %>% 
  sort(decreasing = FALSE) %>% 
  plot()

Which gives me:

But not sure if this is correct. More specifically I want to have a logarithmic curve with numbers on the x-axis and the topic names on the y-axis of the plot.

> dput(head(df$title))
c("ACID?", "Week 2", "Week 2_1", "Are we talking ACID?", "Where has the reading material gone?", 
"I like, I wish...")