50 POIN DILARANG KERAS HANYA UNTUK MENGAMBIL POIN U1, U2, U3, U4 dan U5 adalah lima suku pertama deret geometri. Jika logU1 + logU2 - log U3 + log U4 + log U5 =

[tex]\log U_1 + \log U_2 - \log U_3 + \log U_4 +\log U_5 = 5\log 3 \\ \log(\frac{U_1\times U_2\times U_4\times U_5}{U_3})=5\log 3 \\ U_4=ar^3=12 \\ U_1=a, U_2=ar,U_3=ar^2,U_5=ar^4 \\ \log(\frac{a\times ar\times ar^2\times ar^4}{ar^2})=5\log 3 \\ \log(\frac{a^4r^7}{ar^2})=5\log 3 \\ \log(a^3r^5)=^5\log 3 \\ \ast \\ ar^3=12 \\ a^3r^9=12^3 \\ \\ \log(12^3\times r^{-4})=5\log 3 \\ \log(\frac{1728}{r^4})=\log 3^5 \\ \frac{1728}{r^4}=3^5 \\ r^4=\frac{1728}{243} \\ r^4=\frac{64}{9} \\ r^2=\frac{8}{3}[/tex]
[tex]r=\pm\sqrt{\frac{8}{3}}=\pm2\sqrt{\frac{2}{3}} \\ \\ \\ U_5=U_4\times r \\ U_5=12\times\pm2\sqrt{\frac{2}{3}} \\ U_5=\pm24\sqrt{\frac{2}{3}} = \pm24\frac{\sqrt{2}}{\sqrt{3}}=\pm24\frac{\sqrt{6}}{3} \\ U_5=\pm 8\sqrt{6}[/tex]