Question 117717
{{{log(10,(sqrt(x^3-9)))=2}}} Start with the given equation.  Note: Since you did not specify a base, this means that we're going to use the default base 10.



{{{10^(2)=sqrt(x^3-9)}}} Rewrite the equation using the property: {{{log(b,(x))=y}}} ====> {{{b^y=x}}}



{{{100=sqrt(x^3-9)}}} Evaluate {{{10^(2)}}} to get {{{100}}}



{{{10000=x^3-9}}} Square both sides



{{{10009=x^3}}} Add 9 to both sides



{{{root(3,10009)=x}}} Take the cube root of both sides




So our answer is {{{x=root(3,10009)}}} which is approximately {{{x=21.5508082663667}}}