Question 423933
first some basic rules to remember:

      Log Rules:

      1) {{{logb(mn) = logb(m) + logb(n)}}}

      2) {{{logb(m/n) = logb(m) - logb(n)}}}

      3) {{{logb(mn) = n*logb(m)}}}


you have:

{{{log(x)+log(2x)=2}}}.....so, use the rule number 1


{{{log(x(2x))=2}}}.......I assume the base is {{{10}}}...By the definition of the logarithm implies


{{{(x(2x))=10^2}}}


{{{2x^2=100}}}


{{{x^2=100/2}}}


{{{x^2=50}}}


{{{x=sqrt(50)}}}


{{{x=sqrt(2*25)}}}


{{{x=5sqrt(2)}}}