Question 1005505

{{{log(2,(x^2-11))-log(2,(2x+5))=1}}}


{{{log(2,(x^2-11)/(2x+5))=1}}}......change the base to base {{{10}}}


{{{log((x^2-11)/(2x+5))/log((2))=1}}}


{{{log((x^2-11)/(2x+5))=1*log((2))}}}


{{{log((x^2-11)/(2x+5))=log((2))}}}.........if log same, then


{{{(x^2-11)/(2x+5)=2}}}....solve for {{{x}}}


{{{x^2-11=2(2x+5)}}}


{{{x^2-11=4x+10}}}


{{{x^2-11-4x-10=0}}}


{{{x^2-4x-21=0}}}......factor completely


{{{x^2-7x+3x-21=0}}}


{{{(x^2-7x)+(3x-21)=0}}}


{{{x(x-7)+3(x-7)=0}}}


{{{(x-7)(x+3) = 0}}}


solutions:

{{{x=7}}}

{{{x=-3}}}=> this is a solution only if assuming a complex-valued logarithm