log (x + 17) - log (x - 1) + log (x) = 1

Assuming base for log is 10:

log (x + 17) - log (x - 1) + log (x) = 1

[Log A + Log B - Log C = Log [(AB)/C] and 1 = Log 10 , assuming base is 10]

Log [(x +17)x/(x -1) ] = Log 10

(x +17)x/(x -1) = 10

x(x +17) = 10(x -1)

Solve this quadratic equation.