You actually looked at the entire graph and not just a limited part? I don't believe that! What do you know about derivatives? Can you show that the derivative of e^x is larger than the derivative of Mx? You say "e^x is a much greater increasing function" but that is only true for very large x. You should be able to say exactly for what values of x the slope of Mx is larger than the slope of e^x and for what values of x it is less.

That doesn't even make sense. M is a constant and e^x depends on x. It certainly is NOT true if x is any small number!M is a large number, so M=e^x approximately

NO! That would be saying "A= log M+ log A" and you have no reason to think that., so lnM = x approximately

A = logM + y

so y=logA

Thanks