4^(a) =5 6^(c)=7 5^(b)=6 7^(d)=8 Berapakah a⋅b⋅c⋅d jika seperti ketentuan di atas ? (A) 1 (B) 3/2 (C) 2 (D) 5/2 (E) 3

<p>Jawab: B</p><p>Pembahasan:</p><p>Ingat konsep berikut!</p><ul><li>Jika diketahui a^b = c maka ^alog c = b.</li><li>^alog b . ^blog c . ^clog d . ^dlog e = ^alog e.</li><li>^{a^n}log b^m= m/n ^alog b.</li><li>^alog a = 1</li></ul><p>Dengan menggunakan konsep di atas, diperoleh</p><p>4^a = 5 maka ⁴log 5 = a.</p><p>6^c = 7 maka ⁶log 7 = c.</p><p>5^b = 6 maka ⁵log 6 = b.</p><p>7^d = 8 maka ⁷log 8 = d.</p><p>Oleh karena itu,</p><p>a⋅b⋅c⋅d = ⁴log 5 . ⁵log 6 . ⁶log 7 . ⁷log 8</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = ⁴log 8</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = ^{2^2}log 2³</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 3/2 ²log 2</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 3/2 . 1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 3/2</p><p>&nbsp;</p><p><strong><u>Jadi, jawaban yang benar adalah B.</u></strong></p>