Find the indicated $limit.$ Note that $l\text{'}Hpital\text{'}s$ rule may not apply $or$ may

require more than one application. Use $-or$ when appropriate.

$\underset{x}{lim}\frac{e^{-x}}{ln(1+3e^{-x})}$

Select the correct choice below and, $if$ necessary, fill $in$ the answer box $to$

complete your choice.

$A.\underset{x}{lim}\frac{e^{-x}}{ln(1+3e^{-x})}=$

$(Typean$ exact answer $in$ simplified form.$)$

$B.$ The $limit$ does not exist.