Nilai x mempunyai pertidaksamaan [tex]\large\bf{\sqrt[3]{\frac{1}{9^{2x}}}\ \textgreater \ \frac{\le.... Question from @Sinogen

May 2022 2 12 Report

Nilai x mempunyai pertidaksamaan
[tex]\large\bf{\sqrt[3]{\frac{1}{9^{2x}}}\ \textgreater \ \frac{\left(27^{x}\right)^{2}}{81^{x-2}}}[/tex]
adalah...
[tex]\bf{A.\ \ x\ \textgreater \ -\frac{12}{5}}[/tex]
[tex]\bf{B.\ \ x\ \textless \ -\frac{12}{5}}[/tex]
[tex]\bf{C.\ \ x\ \textgreater \ \frac{4}{5}}[/tex]
[tex]\bf{D.\ \ x\ \textgreater \ -\frac{4}{5}}[/tex]
[tex]\bf{E.\ \ x\ \textless \ -\frac{4}{5}}[/tex]

[tex]\small\boxed{\tt{Note_{1}=Jawablah\ dengan\ usaha\ sendiri}}[/tex]
[tex]\small\boxed{\tt{Note_{2}=Dilarang\ nyalin\ jawaban\ maupun\ copas\ dari\ web}}[/tex]
[tex]\small\boxed{\tt{Note_{3}=Jaga \ Kesehatan \ yah}}[/tex]

Terimakasih ^^

BlackRanger

JAWABAN

Jawaban yang tepat untuk pertanyaan tersebut adalah B. x < -12/5.

CARA

$\sqrt[3]{\frac{1}{9^{2x}}} > \frac{(27^{x})^{2}}{81^{x-2}}\\\sqrt[3]{9^{-2x}} > \frac{27^{2x}}{81^{x-2}}\\9^{-2x} > (\frac{27^{2x}}{81^{x-2}})^{3}\\9^{-2x} > \frac{27^{6x}}{81^{3x-6}}\\(3^{2})^{-2x} > \frac{(3^{3})^{6x}}{(3^{4})^{3x-6}}\\3^{-4x} > \frac{3^{18x}}{3^{12x-24}}\\3^{-4x} > 3^{18x-(12x-24)}\\3^{-4x} > 3^{18x-12x+24}\\-4x > 18x-12x+24\\-4x > 6x+24\\-10x > 24\\x < -\frac{24}{10}\\x < -\frac{12}{5} (B)$