Answer:
x=6 x=3
Step-by-step explanation:
2logx-log(x-2)=2log3
We know that a log b = log b^a
logx^2-log(x-2)=log3^2
logx^2-log(x-2)=log9
subtract log 9 from each side
logx^2-log(x-2)-log9=0
We know that log a - log b = log (a/b)
log(x^2/9(x-2))=0
Raise each side to the power of 10 to get rid of the log
10 ^log(x^2/9(x-2))= 10 ^0
10^ log cancels and 10^0 =1
(x^2/9(x-2))=1
Multiply each side by 9(x-2)
x^2 =9(x-2)
Subtract 9(x-2) from each side
x^2 - 9(x-2) = 9(x-2) - 9(x-2)
x^2 - 9(x-2) = 0
Distribute
x^2 - 9x +18 = 0
Factor
(x-6) (x-3) =0
Using the zero product property
x-6 =0 x-3 =0
x=6 x=3
