Question 116597
{{{log( 2, x+2)=log( .5, 2)}}} Start with the given equation



{{{log( 2, x+2)=-1}}} Evaluate {{{log( .5, 2)}}} to get -1



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



{{{1/2^(1)=x+2}}} Rewrite {{{2^(-1)}}} as  {{{1/2^(1)}}}



{{{1/2=x+2}}} Evaluate {{{1/2^(1)}}} to get {{{1/2}}}



{{{1/2-2=x+cross(2-2)}}} Subtract 2 from both sides



{{{-3/2=x}}} Combine like terms


So our answer is {{{x=-3/2}}}