Log whose base is 5:
log5(x−11)+log5(x−6)=2
=> log5{(x - 11)*(x - 6)} Since, log |m| + log |n| = log|mn|
=> log5{x^2 - 17*x + 66} = 2
On taking antilog both side we get,
=> x^2 - 17*x + 66 = 5^2
=> x^2 - 17*x + 66 = 25
Now on solving the above quadratic equation we get:
x= 17/2 + (5*sqrt(5))/2 or
x = 17/2 - (5*sqrt(5))/2