Question 173596
Log_6 - log_6(x-1)= 1 
Use the property of subtraction for logs. 
I will use log_6 to mean "log base 6." 
log_6(1/(x - 1) = 1 
Remove the word log and raise 6 to the value as given on the other side of the equation. 
6^1 = 1/(x - 1) 
6 = 1(x - 1) 
Solve for x. 

6(x - 1) = 1 
6x - 6 = 1 
6x = 6 + 1 
6x = 7 
x = 7/6 
x = 1.2