Penjelasan dengan langkah-langkah:

Logaritma

nomor (2)

= (³log² 12 - ³log² 4)/(³log 48)

= ((³log 12 + ³log 4)(³log 12 - ³log 4)/(³log 48)

= (³log(12x4)(³log(12/4)) / (³log 48)

= (³log 48)(³log 3)/(³log 48)

= ³log(3)

= 1

nomor (3)

Jika ²⁷log(5) = r ---> 3³log(5) = ⅓ . ³log(5) = ³log(5) = 3r

Maka:

= ⁵log(81)

= ³log(81)/ ³log(5)

= ³log(3⁴) / 3r

= 4/3r

nomor (4)

= ³log(4). ²log(√5) . ⁵log(1/27)

= ³log(2²) . ²log(5^½) . ⁵log(3^-3)

= 2.³log(2) . (½). ²log(5). (-3). ⁵log(3)

= (2 . ½ . (-3)) . (³log(2) . ²log(5) . ⁵log(3))

= (-6/2). (³log (3))

= -3 . 1

= -3

nomor (5)

= ²log(12) + ⁷log(14) - ²log(3) - ⁷log(2)

= ²log(12/3) + ⁷log(14/2)

= ²log(4) + ⁷log(7)

= ²log(2²) + 1

= 2 + 1

= 3

Rumus:

a log(aⁿ) = n

a log(m) + a log(n) = a log(mn)

a log(m) - a log(n) = a log(m/n)

aⁿ log(a^m) = m/n