How do you solve x = log3(77+log3(77+log3(77+...)))) ?

Question

The original question is 3^x - x = 77. By a little simplifying, I got x = log3(77+x) and by substituting I noted that I could obtain a infinite sequence for x = log3(77+log3(77+log3(77+...)))). How do I go about solving this sequence?

Answer 1

For 3^x - x = 77 I would recommend using a Graphing Calculator; find intersection of two graphs:

f(x) = 3^x

g(x) = x+77.