Jika x > 0 dan y > 0, maka nilai 9 - log^2 x^3 y^3 : 6 + 2 log x^12 y^6 - log x^30 y^18 A. log 10xy B. 3 log 10xy C. 9 log 10xy D. 3 + log 10xy E. 9 + log 10xy

(9 - log^2 x^3.y^3) / (6 + 2 log x^12.y^6 - log x^30.y^18)
= (3 + log x^3.y^3)(3 - log x^3.y^3) / (6 + log (x^12.y^6)^2 - log x^30.y^18)
= (3 + log x^3.y^3)(3 - log x^3.y^3) / (6 + log (x^24.y^12)/(x^30.y^18))
= (3 + log x^3.y^3)(3 - log x^3.y^3) / (6 + log x^-6y^-6)
= (3 + log x^3.y^3)(3 - log x^3.y^3) / (6 + log (x^3.y^3)^-2)
= (3 + log x^3.y^3)(3 - log x^3.y^3) / (6 - 2 log x^3.y^3)
= (3 + log x^3.y^3)(3 - log x^3.y^3) / 2(3 - log x^3.y^3)
= 1/2 (3 + log x^3.y^3)

= 1/2 (log 10^3 + log x^3.y^3)
= 1/2 log 10^3.x^3.y^3
= 1/2 log (10xy)^3
= 3/2 log (10xy)

= 3 log √(10xy)

Tak ada di option