Hello, I want to represent the logarithm of different base numbers,

but the ampl explanation document seems to only have log10 and log,

I want to represent the constraint how to do?

Hello, I wrote this is wrong, there is a mistake, may I ask how to express the above formula

\log_\frac{1}{10} (e^x+10^R) has the same value as -\log_{10} (e^x+10^R), so you can write this constraint as

y + R \leq -\log_{10} (e^x+10^R)

Hello There is an error when x goes to infinity, how do I set the upper and lower bounds of y

You can add a constraint to your AMPL model to set a lower bound or an upper bound on a variable, or on an expression involving variables.