Question 865373
{{{4^(3x-2)=6^x}}} Start with the given equation.



{{{ln(4^(3x-2))=ln(6^x)}}} Take the natural log of both sides.



{{{(3x-2)*ln(4)=x*ln(6)}}} Pull down the exponents.



{{{3x*ln(4)-2*ln(4)=x*ln(6)}}} Distribute.



{{{3x*ln(4)=x*ln(6)+2*ln(4)}}} Add {{{2*ln(4)}}} to both sides.



{{{3x*ln(4)-x*ln(6)=2*ln(4)}}} Subtract {{{x*ln(6)}}} from both sides.



{{{x(3*ln(4)-ln(6))=2*ln(4)}}} Factor out x



{{{x=(2*ln(4))/(3*ln(4)-ln(6))}}} Divide both sides by {{{3*ln(4)-ln(6)}}} to isolate x.



{{{x=1.17129021301953}}} Use a calculator to evaluate the right hand side (RHS)



{{{x=1.1713}}} Round to 4 decimal places