Question 748218
{{{ln(x^3)-ln(2-(3/2)x)=ln(2x)}}}


{{{ln(x^3)-ln((4-3x)/2)=ln(2x)}}}........since {{{ln((4-3x)/2)=ln(4-3x)-ln(2)}}}, we will have


{{{ln(x^3)-(ln(4-3x)-ln(2))=ln(2x)}}}

{{{ln(x^3)-ln(4-3x)+ln(2)=ln(2x)}}}


{{{ln(x^3)+ln(2)=ln(2x)+ln(4-3x)}}}


{{{ln(2x^3)=ln(2x(4-3x))}}}

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

{{{cross(2)x^cross(3)=cross(2)cross(x)(4-3x)}}}

{{{x^2=4-3x}}}

{{{x^2+3x-4=0}}}


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


{{{x = (-3 +- sqrt( 3^2-4*1*(-4) ))/(2*1) }}}


{{{x = (-3 +- sqrt( 9+16 ))/2 }}}

{{{x = (-3 +- sqrt(25 ))/2 }}}


{{{x = (-3 +- 5)/2 }}}

solutions:

{{{x = (-3 + 5)/2 }}}

{{{x = 2/2 }}}

{{{x =1 }}}......real solution


{{{x = (-3 - 5)/2 }}}

{{{x = -8/2 }}}

{{{x =-4 }}}.....assuming a complex-valued logarithm