[Logaritma] Diketahui f(n) = 3log4 . 4log5 . . . ^(n-1) log n. Jika, f(a) + f(a^2) + . . . + f(a^9) = f(a) . f(a^5) Maka, a1 . a2 ? . . . Untuk lebih jelasnya,

[tex] f(n) = ^3log4.^4log5. ... .^{n-1}logn \\ f(n) = ^3log n \\ {sifat} {logaritma} \\ {} \\ f(a) + f(a^2) + ... + f(a^9) = f(a).f(a^5) \\ ^3log a + ^3log a^2 + ... + ^3log a^9 = ^3log a . ^3log a^5 \\ ^3log(a.a^2. ... .a^9) = ^3log a.(5.^3log a) \\ ^3log(a^45) = 5.(^3log a)^2 \\ 45.^3log a = 5.(^3log a)^2 [/tex]

Anggap ³log a = x

45x = 5x²
9x = x²
0 = x² - 9x
0 = x(x - 9)

x1 = 0
dan
x2 = 9


x1 = 0
³log a1 = 0
a1 = 3^0
a1 = 1

x2 = 9
³log a2 = 9
a2 = 3^9


a1 . a2
= 1 . 3^9
= 3^9
[C]