This is a dichotomous outcome, not a Likert scale. So binary logistic regression is appropriate.

If you will use the likert scale the outcome can't be dichotomous. You will have at least 3 different outcome (satisfied, neither satisfied nor dissatisfied, and dissatisfied). But if you use just 2 variables, the answer of Stephen is appropriated.

Technically, a Likert Scale is the sum, or average, of several 1-5 Agree-Disagree rating scales. (A single Likert Scale item, one question, usually is too blunt an instrument and not much use for anything.) In most social research, Likert scales are assumed to be continuous, interval-scaled measures, and they are thus acceptable as dependent variables in multiple regression.

But, as pointed out by Stephen and Wendel, above, if your question is a simple binary response, or you have transformed a rating scale into a binary response, such as 0=unsatisfied 1=satisfied, then the appropriate method is binary logistic regression.

yes thank you for clarification.

Thank you all.

yes I transformed a rating scale into a binary response i.e; 0=unsatisfied 1=satisfied