Solve for X
log 4x - log (2x-3) = log 6
Solve for X log 4x - log (2x-3) = log 6
\(log( 4x) - log (2x-3) = log 6\\ log(2* 2x) - log (2x-3) = log 6\\ log(2)+log(2x) - log (2x-3) = log3+log2\\ log(2x) - log (2x-3) = log(3)\\ log(\frac{2x}{2x-3})=log3\\ \frac{2x}{2x-3}=3\\ 2x=6x-9\\ -4x=-9\\ x=2\frac{1}{4}\)
There is a quicker way to do this. Since log( a/b ) = log a - log b
then log(4x) - log (2x-3) can be written as
log (4x)/(2x-3)
So log(4x)/(2x-3) =log 6
then
(4x)/(2x-3) =6 by equivalence
4x = 12x-18
8x=18
x=18/8=9/4
