I have a logistic regression model, where one of my variables is logged. It is of the following form:
$\ln(\frac{p}{1-p}) = B_1\ln(X) + B_2Y + ... + \epsilon$ , where $\epsilon$ is an error term.
I am aware that I can interpret my results as "holding all else constant, an $e$-fold increase in $X$ will cause an $e^{B_1}$-fold increase in the estimated probability $\hat{p}$." My question is: Can you generalize this to arbitrary increases in $x$, without changing the natural log to another logarithm? For example, how would I estimate the impact of a $10\%$ increase in $x$? Or a doubling of $x$?
