Question

How do you simplify `Ln(1-e^-x)`?

Answer 1

We can write the argument as a fraction after getting rid of the negative exponent:

`ln(1-e^-x)=ln(1-1/e^x)=ln((e^x-1)/e^x)`

From here, use `ln(a/b)=ln(a)-ln(b)` and `ln(e^x)=x`:

`=ln(e^x-1)-ln(e^x)=color(blue)(ln(e^x-1)-x`

I don't know if this is a simplification per se, but it's definitely a valid way to rewrite the function.