I have log transformed my data in R, but I want to find out what the 'original' unlogged value would be I have a binomial glm modelling the probability of the occurrence of otter roadkill hotspots. My data were not normally distributed therefore to adhere to model assumptions I log transformed all of my variables in R.
The scale of the x-axis on my model prediction graphs are therefore logged. I have a graph looking at the association between roadkill hotspots and distance to nearest road-river crossing. In my model reporting, I have said 'At locations 5 or more metres from a road-river crossing, hotspots were very unlikely to occur.' I would like to know that the value 5 is unlogged, and add this to my figure caption. 5 metres is a tiny distance and in real life and based off of my data this is more likely to be say something like 750m.
Please could anyone tell me how I could find out what this value is unlogged?! To transform the data I just did log(dframe$rivercrossing). Have added my graph for context which has the logged scale.
I can't seem to find any answers on this, I'm stumped! Any help would be massively appreciated. Thanks!
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 A: 
I have a binomial glm modelling the probability of the occurrence of otter roadkill hotspots. My data were not normally distributed therefore to adhere to model assumptions I log transformed all of my variables in R.

For the next time (or maybe when you want to redo the analysis), this log transform is not necessary for the reason to get the data shaped according to the assumption that it must be normally distributed.
The problem situation that you refer to is the case when the error distribution is not following a normal distribution.
See: What if residuals are normally distributed, but y is not? and Where does the misconception that Y must be normally distributed come from?
In fact, the binomial GLM model doesn't assume normally distributed residuals either. That particular model is for data where the response variable has only values 0 and 1.
However, log transforming the x coordinate might still be done for visualisation or in order to fit a specific trendline or function.


The scale of the x-axis on my model prediction graphs are therefore logged. I have a graph looking at the association between roadkill hotspots and distance to nearest road-river crossing. In my model reporting, I have said 'At locations 5 or more metres from a road-river crossing, hotspots were very unlikely to occur.' I would like to know that the value 5 is unlogged, and add this to my figure caption. 5 metres is a tiny distance and in real life and based off of my data this is more likely to be say something like 750m.

The inverse of taking the logarithm is exponentiation. Often the log refers to either the natural logarithm or a logarithm with base 10. So the value 5 will refer to $$10^5 = 100000 \text{ meters } = 100 \ \text {km}$$ or to $$\exp(5) = e^5 \approx 148 \text{ meters }$$

To make your graph easier to read you could transform all x values back in the plotting and plot the x-axis as a log-scale. Then you have the same shape as in your current graph but with the labels transformed to the actual values in meters.
See below for example:

