[tex]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=-\dfrac{1}{2}}[/tex]
