Question

how do I solve for 2e^x=5-e^x

Answer 1

add e^x to both sides divided both sides by 2 take the natural logarithm of both sides so you get $$\ln(\frac{5}{3})$$

Answer 2

2e^x=5-e^x , so 3e^x=5 i.e. e^x=5/3 . Taking Natural log on both sides gives x=ln(5/3)