Question

Whats the domain for this equation?

Answer 1

Strictly speaking an equation does not have a domain. A function does. Though it may make sense to speak about a solution set to this equation over a domain.

The following could be helpful towards an answer: The equation has two sides. The left hand side is a non-linear function and the right hand side is a line with slope -1 and y-intercept of 1.

The function$\log_5(6-5^x)$ has a domain over all Reals x for which it holds $6-5^x > 0 \\6 > 5^x\\\log_5 6 > x$ so the domain of the nonlinear function is $-\infty$.

The domain of the linear function 1-x is all Reals: $-\infty$

So, together you could say the equation's solutions are defined over the domain $-\infty$.

Lmk if you have questions.