If log x=a and log y=b

Question

what is log(100x^2/y^3) in terms of a and b?

Answer 1

GIVEN is log(100x^2/y^3)

                log 100x^2 /  log y^3

             ( log 100 +log x^2) / log y^3

             ( log 10^2 +log x^2  )/ log y^3

            ( 2 log 10 + 2 log x )/ 3 log y

           2( log 10 +log x ) / 3 log y

       2/3( log 10x / log y)

       2/3 log 10x/y

       2/3 log 10a/b