Answer:
x= 3/2
Step-by-step explanation:
log3(x) + log3(2x-1) =1
We know that log a+log b = log ab
log3((x)(2x-1)) = 1
Raise each side to the base 3
3^log3((x)(2x-1)) = 3^1
x*(2x-1) = 3^1
Distribute
2x^2 -x = 3
Subtract 3 from each side
2x^2 -x-3 = 3-3
2x^2 -x-3 = 0
Factor
(2x-3) (x+1) =0
Using the zero product property
2x-3 =0 x+1 =0
2x=3 x=-1
x = 3/2 x =-1
But we cannot take logs of negatives ( as we see when we put it back in the original equation)
so x=-1 is an extraneous solution
x= 3/2
