Question 313667
{{{log(10,(5x-1)) + log(10,(x+2))=1}}}
{{{log(10,(5x-1)(x+2))=1}}}
{{{(5x-1)(x+2)=10}}}
{{{5x^2+9x-2=10}}}
{{{5x^2+9x-12=0}}}
Use the quadratic formula,
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{x = (-9 +- sqrt( (-9)^2-4*5*(-12) ))/(2*5) }}} 
{{{x = (-9 +- sqrt( 81+240))/(10) }}} 
{{{x = (-9 +- sqrt( 321))/(10) }}} 
Only the positive solution will be considered since the log function requires non-negative arguments. 
{{{x = (-9 + sqrt( 321))/(10) }}} or approximately,
{{{highlight(x= 0.8916)}}}