Tentukan himpunan penyelesaian dari setiap persamaan logaritma berikut.

<p>Jawaban : {2,8}</p><p>&nbsp;</p><p>Ingat :</p><p>Persamaan logaritma :</p><p>^alog aⁿ = n</p><p>aⁿ log a^m = m/n . ^alog a</p><p>^alog b - ^alog c = ^alog b/c</p><p>^alog b = c ---&gt; a^c = b</p><p>&nbsp;</p><p>Pembahasan :</p><p>x^²log x = x⁴/8</p><p>Ubah persamaannya dengan kalikan ²log</p><p>&nbsp;</p><p>x^²log x = x⁴/8</p><p>--------------------- x (²log)</p><p>²log x^²log x = ²log x⁴/8</p><p>²log x . ²log x = &nbsp;²log x⁴- &nbsp;²log 2³</p><p>&nbsp;</p><p>Misalkan &nbsp;²log x = a</p><p>a . a = 4a - 3</p><p>a² = 4a - 3</p><p>a² - 4a + 3 = 0</p><p>(a - 3)(a - 1) = 0</p><p>a - 3 = 0 &nbsp; atau &nbsp;a - 1 = 0</p><p>a = 3 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;a = 1</p><p>&nbsp;</p><p>²log x = a</p><p>²log x = 3</p><p>2³ = x</p><p>x = 8</p><p>&nbsp;</p><p>²log x = 1</p><p>2¹ = x</p><p>x = 2</p><p>Hp = {2, 8}</p><p>&nbsp;</p><p>Oleh karena itu, Himpunan Penyelesaian nya adalah {2, 8}</p>