Jika log(x - y) = log 3 · ⁹log 4 dan 2^(x - 1) = 4^(y + x) maka y = .... A. -2 B. -1 C. 0 D. 1 E. 2

<p>Jawaban yang benar adalah B.</p><p>&nbsp;</p><p>Konsep:</p><p>^{a^b} logc^d = d/b x ^alogc</p><p>^alogb × ^blog c = ^alog c&nbsp;</p><p>^alog f(x) = ^alog g(x) &gt;&gt; f(x) = g(x)</p><p>(a^m)ⁿ = a^m.n</p><p>&nbsp;</p><p>Jika tidak dituliskan basisnya, maka nilai basis log = 10</p><p>¹⁰log(x - y)</p><p>¹⁰log(x - y) = ¹⁰log 3 · ⁹log 4&nbsp;</p><p>¹⁰log(x - y) = ¹⁰log 3 · 3^{^3}log 2²</p><p>¹⁰log(x - y) = ¹⁰<i>log 3 · ³</i>log 2 × ²/₂</p><p>¹⁰log(x - y) = ¹⁰log 2 × 1</p><p>¹⁰log(x - y) = ¹⁰log 2 ⇔ x - y &nbsp;= 2 .... (1)</p><p>&nbsp;</p><p>&nbsp;2^{(x - 1)} = 4^{(y + x)}</p><p>&nbsp;2^{(x - 1)} = (2²)^{(y + x)}</p><p>&nbsp;2^{x - 1} = 2^{2y + 2x}</p><p>&nbsp;x - 1 = 2y + 2x</p><p>x + 2y = -1 ....(2)</p><p>&nbsp;</p><p>Kita lakukan eliminasi pada kedua persamaan diatas.</p><p>&nbsp;x - y &nbsp;= 2&nbsp;</p><p>x + 2y = -1</p><p>---------------- <strong>-</strong></p><p>-3y = 3</p><p>y = -1</p><p>&nbsp;</p><p>Jadi, nilai y adalah -1.</p>