Question

Solve the Equation for x:

e^xe^(x+1)=1

Answer 1

X = -1/2 is the final answer

Answer 2

`e^x\cdot e^(x+1)=1\qquad\text{use}\ a^n\cdot a^m=a^(n+m)\\\\e^(x+x+1)=1\\\\e^(2x+1)=1\qquad\text{use}\ a^0=1\\\\e^(2x+1)=e^0\iff2x+1=0\qquad\text{subtract 1 from both sides}\\\\2x=-1\qquad\text{divide both sides by 2}\\\\\boxed{x=-(1)/(2)}`