I need to extract the real lethal doses from a sigmoidal dose curve from a probit model. The doses (mg) are the X-Axis and were log transformed. Model parameters were not reported, only that the true values of the two X's (bottom right) are 7.14 mg and 12.2mg, which on the graph have X-axis values of 0.390 and 0.717, respectively. From this information, is there a way to transform the X-axis into the real (mg) values?
If the information in your post was all correct, yes, you could work out what the dosages were for any x-value:
If those x-values are truly on a log scale then their difference will be proportional to the log of the ratio of the dosages; this would allow us to work out the base of the logs:
> log(c(12.2/7.14))  0.5357232 > 0.717-0.390  0.327 > exp(0.5357/0.327)  5.146034
I highly doubt that the logs were in that base, so I strongly doubt the axis shows log-dosages (note that a change of units would not change the log of the ratio, so it's not simply a log scale as your post suggests)
Perhaps some additional transformation has been applied to the x-axis.