Solve the following equation for x:

log₆ (x - 2) + log₆ (x + 3) = 1

Solve the following equation for x:

log (x + 1) + log (x - 1) = log 11 + 2log 3

If a = 1 + log_x yz, b = 1 + log_y zx and c = 1 + log_z xy, then show that

ab + bc + ca = abc.