Question 132646
{{{log(4,(3x^2 - 2x)) = log(6,36)}}}
{{{log(4,(3x^2 - 2x)) = log(6,6^2)}}}
The right side = {{{2}}}
{{{log(4,(3x^2 - 2x)) = 2}}}
This says "The exponent to the base 4 which gives me {{{3x^2 - 2x}}}
is 2, so
{{{4^2 = 3x^2 - 2x}}}
{{{3x^2 - 2x - 16 = 0}}}
Solve using quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (-(-2) +- sqrt( (-2)^2-4*3*(-16) ))/(2*3) }}}
{{{x = ( 2 +- sqrt(4 + 192 ))/ 6 }}}
{{{x = ( 2 +- 14)/ 6 }}}
{{{x = 8/3}}}
{{{x = -2}}}
check answers:
{{{log(4,(3x^2 - 2x)) = log(6,36)}}}
{{{log(4,3*(8/3)^2 - 2*(8/3)) = log(6,36)}}}
{{{log(4, (64/3 - 16/3)) = 2}}}
{{{log(4, 16) = 2}}}
True
{{{log(4,(3x^2 - 2x)) = log(6,36)}}}
{{{log(4,(3*(-2)^2 - 2*(-2))) = log(6,36)}}}
{{{log(4,(12 + 4))) = log(6,36)}}}
{{{log(4,16) = 2}}}
True