Tentukan himpunan penyelesaian dari setiap persamaan logaritma berikut.

Jawaban: HP = {4} Konsep! * 1/(ªlog b) = ^(b) log a * ªlog (b.c) = ªlog b + ªlog c * ^(a)^(b) log c^(d) = (d/b) ªlog c * ªlog b = (^(n)log b)/(^(n)log a) * ªlog b^(n) = n.ªlog b * ªlog a = 1 * ªlog x = b, maka x = a^(b) * Syarat numerus > 0 Pembahasan: (1/(^(x – 2)log x) + ^(x) log (x – 3) + ^(x) log 4 = 1/(⁸log x) ^(x) log (x – 2) + ^(x) log (x – 3) + ^(x) log 4 = 1/(⁸log x) ^(x) log ((x – 2)(x – 3)(4))(⁸log x) = 1 ^(x) log ((x² – 5x + 6)(4))(^(2³) log x) = 1 ^(x) log (4x² – 20x + 24)(⅓)(²log x) = 1 ^(x) log (4x² – 20x + 24)(²log x) = 3 (²log (4x² – 20x + 24)/²log x)(²log x) = 3 ²log (4x² – 20x + 24) = 3 ²log (4(x² – 5x + 6)) = 3 ²log 4 + ²log (x² – 5x + 6) = 3 ²log 2² + ²log (x² – 5x + 6) = 3 2.²log 2 + ²log (x² – 5x + 6) = 3 2.1 + ²log (x² – 5x + 6) = 3 2 + ²log (x² – 5x + 6) = 3 ²log (x² – 5x + 6) = 3 – 2 ²log (x² – 5x + 6) = 1 x² – 5x + 6 = 2¹ x² – 5x + 6 = 2 x² – 5x + 6 – 2 = 0 x² – 5x + 4 = 0 (x – 4)(x – 1) = 0 x = 4 atau x = 1 Syarat numerus x – 3 > 0 x > 3 Jadi, himpunan penyelesaiannya adalah HP = {4}.