This should be a rather simple problem however I am having difficulty getting this simplified.
If I need to simplify the expression $$ \ln(A/B)+C$$ My first step is $$ A/B + e^c$$ However MATLAB and Wolfram say the two are not equal. Why is this and how do I simplify it?
With a concrete counterexample it might be more apparent: let $A=10, B=1, C=\ln(10)$. Your expression above reads as $$ \ln(10)+\ln(10)=2\ln(10)=\ln(10^2)=\ln(100) $$ but the other one reads as $$ 10 + 10 = 20 $$ as you can see there are quite a difference between one and the other.
The point is that you don't simplify an expression by itself, but instead you simplify an equation by changing both terms so they are equal after the simplification whenever they were equal before the simplification. So you take an equation, let's see $$ \ln(A/B)+C = K $$ and try to simplify it: $$ something = something else $$ The natural way is tho take the exponent of both sides: $$ e^{\ln(A/B)+C} = e^K $$ which is $$ e^{\ln(A/B)}e^{C} = e^K $$ thus $$ \frac{A}{B}e^{C} = e^K $$ Note that it's a product and not a sum.