2^(x) + 3 × 2^(y) = 3 2^(2x) - 9 × 2^(2y) = 6 Jika diperoleh solusi x = p dan y = q, berapakah nilai p - q? A. ² log 9 B. 5/12 C. ² log 15 D. ² log 7/3 E. 7/3

<p>Jawaban : C. ² log 15</p><p>&nbsp;</p><p>Ingat!</p><p>(a^(m))^(n) = a^(mn)</p><p>Jika ^(a) log (b) = c, maka b = a^(c)</p><p>^(a) log (b) - ^(a) log (c) = ^(a) log (b/c)</p><p>&nbsp;</p><p>Diketahui&nbsp;</p><p>2^(x) + 3 × 2^(y) = 3 ... (i)</p><p>2^(2x) - 9 × 2^(2y) = 6 ... (ii)</p><p>&nbsp;</p><p>Misalkan a = 2^(x) dan b = 2^(y)</p><p>&nbsp;</p><p>Dari persamaan (i) diperoleh</p><p>2^(x) + 3 × 2^(y) = 3</p><p>a + 3 × b = 3</p><p>a + 3b = 3</p><p>a = 3 - 3b</p><p>&nbsp;</p><p>Dari persamaan (ii) diperoleh</p><p>2^(2x) - 9 × 2^(2y) = 6</p><p>(2^(x))^(2) - 9 × (2^(y))^(2) = 6</p><p>a^(2) - 9 × b^(2) = 6<br>(3 - 3b)^(2) - 9 b^(2) = 6</p><p>9 - 18b + 9b^(2) - 9 b^(2) = 6</p><p>9 - 18b = 6</p><p>3 = 18b</p><p>b = 3/18</p><p>b = 1/6</p><p>2^(y) = 1/6</p><p>y = ^(2) log (1/6)</p><p>&nbsp;</p><p>a = 3 - 3b</p><p>a = 3 - 3 × 3/18</p><p>a = 3 - 1/2</p><p>a = 5/2</p><p>2^(x) = 5/2</p><p>x = ^(2) log (5/2)</p><p>&nbsp;</p><p>Jika diperoleh solusi x = p dan y = q, maka nilai&nbsp;</p><p>p - q</p><p>= x - y</p><p>= ^(2) log (5/2) - ^(2) log (1/6)</p><p>= ^(2) log ((5/2)/(1/6))</p><p>= ^(2) log (15)</p><p>&nbsp;</p><p>Jadi, p - q = ^(2) log (15)</p><p>Oleh karena itu, jawaban yang benar adalah C.</p>