Jika x1 dan x2 merupakan akar-akar persamaan eksponen 5(25^x) - 16(5^x) + 3 = 0, hitunglah: x1^4 - x2^4

<p>Jawaban yang benar adalah 1 – ⁵log² 3.&nbsp;</p><p>&nbsp;</p><p>Pembahasan :&nbsp;</p><p>Sifat bilangan eksponen&nbsp;</p><p>a^f(x) = a^c → f(x) = c&nbsp;</p><p>&nbsp;</p><p>Prinsip logaritma<br>^a log m = b → a^b = m</p><p>&nbsp;</p><p>Penyelesaian :&nbsp;</p><p>5(25^x) – 16(5^x) + 3 = 0&nbsp;</p><p>5(5^(2x)) – 16(5^x) + 3 = 0&nbsp;</p><p>5 · (5^x)² – 16 · 5^x + 3 = 0&nbsp;</p><p>Misal, 5^x = p&nbsp;</p><p>5 · p² – 16 · p + 3 = 0&nbsp;</p><p>5p² – 16p + 3 = 0&nbsp;</p><p>(5p – 1)(p – 3) = 0&nbsp;</p><p>5p – 1 = 0&nbsp;</p><p>5p = 1&nbsp;</p><p>p = 1/5&nbsp;</p><p>atau&nbsp;</p><p>p – 3 = 0&nbsp;</p><p>p = 3&nbsp;</p><p>&nbsp;</p><p>p = 1/5&nbsp;</p><p>5^x = 1/5&nbsp;</p><p>5^x = 5^(–1)&nbsp;</p><p>x = –1&nbsp;</p><p>&nbsp;</p><p>p = 3&nbsp;</p><p>5^x = 3</p><p>x = ⁵log 3&nbsp;</p><p>&nbsp;</p><p>Akar - akar :&nbsp;</p><p>x1 = -1&nbsp;</p><p>x2 = ⁵log 3</p><p>&nbsp;</p><p>x1⁴ – x2⁴<br>= (–1)⁴ – (⁵log 3)⁴<br>= 1 – ⁵log⁴ 3</p><p>&nbsp;</p><p>Jadi, nilai dari x1⁴ - x2⁴ diatas adalah 1 – ⁵log⁴ 3.</p>