Himpunan penyelesaian dari 2 ³log²x − 5 ³log x + 2 = 0 adalah ..... A. {−½, −2} B. {½, 2} C. {√3, 9} D. {⅓√3, ⅑} E. {3, 9}

<p>Jawab: C</p><p>Pembahasan:</p><p>Ingat!</p><p>a^b= c &nbsp;jika dan hanya jika ^alog c = b.</p><p>Perhatikan bahwa:</p><p>2 ³log²x − 5 ³log x + 2 = 0</p><p>Misal ³log x = p, maka</p><p>2 ³log²x − 5 ³log x + 2 = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2p²-5p+2 = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 2p²-p-4p+2 = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;p(2p-1)-2(2p-1) = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (p-2)(2p-1) = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; p = 2 atau p = 1/2</p><p>Sehingga,</p><p>³log x = 2 &nbsp; &nbsp;maka x = 9</p><p>Dan,&nbsp;</p><p>³log x = 1/2 &nbsp; maka x = √3</p><p>&nbsp;</p><p><strong><u>Jadi, jawaban yang benar adalah C.</u></strong></p>