1. Nilai x yang memenuhi ²log² 3x+ 2 ²log 3x – 3 = 0 adalah

Jawaban:

1. ²log²3x + 2 ²log3x – 3 = 0

misal : p = ²log3x

p² + 2p – 3 = 0

(p + 3) (p – 1) = 0

p = -3 atau p = 1

²log3x = -3 atau ²log3x = 1

Inget bahwa ^a log b = c equivalen dg

a^c = b

shg

²log3x = -3 ===> 3x = 2^(-3)

3x = 1/8

x = 1/24

²log3x = 1 ====> 3x = 2¹

x = 2/3

x yg memenuhi [1/24, 2/3]

2. ²log3 = a, ⁷log3 = b

³log2 = 1/a, ⁷log2 = ⁷log3.³log2

= b . 1/a = b/a

⁶log63 = ⁶log (21 . 3)

= ⁶log21 + ⁶log3

= ⁶log7 + ⁶log3 + ⁶log3

= 1/⁷log6 + 2. 1/³log6

= 1/[⁷log3 + ⁷log2] + 2/[³log3 + ³log2]

= 1/[b + b/a] + 2/[1 + 1/a]

= 1/[ba/a + b/a] + 2/[a/a + 1/a]

= a/(ab + b) + 2a/(a + 1)

= a/b(a + 1) + 2a/(a + 1)

= a/b(a + 1) + 2ab/b(a + 1)

= a(1 + 2b) / b(a + 1)

semoga membantu

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