Question 37816
{{{ log(2-3x) - log(x) = log(2x) }}}
{{{ log((2-3x)/x) = log(2x) }}}


and now raise both sides to power 10:
{{{ (2-3x)/x = 2x }}}
{{{ 2-3x = 2x^2 }}}
{{{ 2x^2 + 3x - 2 = 0 }}}
(2x - 1)(x + 2) = 0
so 2x-1 = 0 or x+2 = 0
so x=1/2 or x=-2


CHECK:
put x=1/2 into {{{ log(2-3x) - log(x) = log(2x) }}} and all th elog terms are fine.


put x=-2 into {{{ log(2-3x) - log(x) = log(2x) }}} and we get {{{ log(8) - log(-2) = log(-4) }}}


and the last 2 log terms are not defined for this. So the answer to the question is x=1/2.


jon.