way out; means of survival; escape route
Refers to a path or means to overcome a difficult situation, often used in phrases like 活路を見出す (find a way out) or 活路を開く (open up a way).
In this recession, we need to find a new way out.
He sought a means of survival in overseas markets.
Amid tough business conditions, they found a way forward through a new venture.
The company opened up a path to survival by expanding into overseas markets.
He sought a way forward through new technology.
逃げ道 emphasizes escaping from danger or blame, whereas 活路 focuses on finding a way to survive or succeed in a difficult situation.
抜け道 often implies a loophole or shortcut (sometimes underhanded), while 活路 has a more positive, effortful connotation of overcoming hardship.
出口 is a literal physical exit, while 活路 is a figurative way out of a difficult or dangerous situation.
developing a way or means; finding a path forward
Compound of 活 (activity, life) and 路 (path, route), literally 'path to life/activity'. The exact historical derivation is uncertain, but the meaning is transparent from the kanji.