Question 950730
{{{log((3x))+log((x-2))=log((x-4))}}}


first use the addition of logs rule [loga + logb is equivalent to log(a*b)]


{{{log((3x(x-2)))=log((x-4))}}}


logs on each side end up cancelling themselves out as long as everything has a log of the same base. 


{{{3x(x-2)=x-4}}}
{{{3x^2-6x=x-4}}}
{{{3x^2-7x+4=0}}}
{{{(3x-4)(x-1)=0}}}


{{{3x-4=0}}}
{{{x=4/3}}}


{{{x-1=0}}}
{{{x=1}}}


The answer is x = 1 and 4/3.