Beautiful. But Sir, if we consider (5x + 1) = m instead of 5x = m, it looks bit simpler. So that the LHS becomes [(5x +1)/5x] ^ (5x + 1) which is [m/(m-1)]^m. We can transform it as [(m-1)/m]^-m. This is equal to (1 - (1/m))^ -m). This also can be written as (1 + (1/(-m))^ -m). This is when compared to the RHS, we get -m = 9 or m = -9. That is 5x + 1 = -9. Solving for x we get x = -2. This is just an inspiration from your work, no new idea. Thank you.
