Question

If ex + e*-1= 2, then x =..

Answer 1

Note: Your equation seems a little unclear. But, I am assuming that your equation is:

$e^x\:+\:e^{-1}=\:2$

Because my solution would still clear your concept about this topic, no matter what the question is.

Answer:

Please check the explanation.

Step-by-step explanation:

Given the equation

$e^x\:+\:e^{-1}=\:2$

subtract $e^{-1}$ from both sides

$e^x+e^{-1}-e^{-1}=2-e^{-1}$

$e^x=2-\frac{1}{e}$

$\ln \left(e^x\right)\:=\ln \:\left(2-\frac{1}{e}\right)$

$\:x\cdot ln\left(e\right)=\ln \:\:\left(2-\frac{1}{e}\right)$

$\:x\cdot 1=\ln \:\left(2-\frac{1}{e}\right)$       ∵ $\:\:\ln \left(e\right)=1$

$x=\ln \:\left(2-\frac{1}{e}\right)$    

$x=0.5$