# How do I back-transfrom my estimates (and confidence intervals) from log10 variables (both independent and dependent) in linear model

I ran linear models for a bunch of variables in R. Both variables are log10 transformed (dependent and independent). I already took a look in some online documents and videos about this but i guess I'm doing something wrong. (https://kenbenoit.net/assets/courses/ME104/logmodels2.pdf, https://www.youtube.com/watch?v=wXC2kViEGz8,https://www.youtube.com/watch?v=OyDfycQ59xo&t=339s)

median(Y)= 1.47 #no log10

median(X)= 3.08 #no log10

estimate= -0.01

confidence interval=(-0-11, 0.08)

Using one of the methods in the videos (my interpretation of the formula was k^b*(med(y)|med(x)^k, were k= is the percent of change choose, b=estimate,med=median)) i did this:

> 10^-0.01*(1.47/3.083^10)
[1] 1.851749e-05


My interpretation is: "for each 10% increase in x we have a change in y of 2e-05". But im sure something goes wrong, the video talk about log not log10. And some points of the equations i didn't knew how to put them in R (the original one looked something like this: k^b1*(med(y|x==3))).