Question 242396
{{{log(2,(3-x))+log(2,(1-2x))=5}}}
{{{log(2,((3-x)(1-2x)))=5}}}
{{{(3-x)(1-2x)=2^5}}}
{{{3-6x-x+2x^2=32}}}
{{{2x^2-7x-29=0}}}
Use the quadratic formula,
{{{x = (-(-7) +- sqrt( (-7)^2-4*(2)*(-29) ))/(2*2) }}} 
{{{x = (7 +- sqrt( 281 ))/(4) }}} 
Two solutions:
{{{x=5.941}}}
{{{x=-2.441}}}
Check the solutions,
{{{log(2,(3-x))+log(2,(1-2x))=5}}}
{{{log(2,(-2.941))+log(2,(-10.882))=5}}}
Negative arguments for logs are not allowed. 
x=5.941 is not a solution.
{{{log(2,(3-x))+log(2,(1-2x))=5}}}
{{{log(2,(5.441))+log(2,(5.882))=5}}}
{{{2.4439+2.5563=5}}}
{{{4.9999=5}}}
Close enough.
x=-2.441