Solve the equation log (little 3) X + log (little6) X = 2

[jupiter_8917]

Solve the equation

log (little 3) X + log (little6) X = 2
the answer is 3.9

Here is what I try
log (little 6)x = log (little 3)x/log (little 3)6 = log (little 3) (x-6)log (little 3)x + log (little 3) (x-6) = 2
log (little3) (x(x-6)) =2
log (little3) (x^2-6x)=3^2

x^2 -6x =9
x^2-6x-9=0

x= 7.2 and -1.2 and of course it is not the right answer

can anyone please explain how do you get 3.9? Thank you

 

[ehild]

Here is what I try
log (little 6)x = log (little 3)x/log (little 3)6 = log (little 3) (x-6)
Thank you

log₆(x)=log₃(x) /log₃(6)- this is right,
but it is not equal to log₃(x-6).

ehild