Question 197261



{{{4*log(3,(-2x))=10}}} Start with the given equation.



{{{log(3,(-2x))=10/4}}} Divide both sides by 4.



{{{log(3,(-2x))=5/2}}} Reduce



{{{3^(5/2)=-2x}}} Rewrite the equation using the property: {{{log(b,(x))=y}}} ====> {{{b^y=x}}}



{{{-(3^(5/2))/2=x}}} Divide both sides by -2.



{{{x=-(3^(5/2))/2}}} Rearrange the equation



{{{x=-(sqrt(243))/2}}} Convert to radical form and simplify



{{{x=-(9*sqrt(3))/2}}} Simplify the square root.



So the solution is {{{x=-(9*sqrt(3))/2}}} which approximates to *[Tex \LARGE x \approx -7.79423]