Nilai dari ^(1/5)logsqrt(27)⋅^(√(3))log25+9^(3log4) adalah ....

Jawaban : 10 Ingat sifat logaritma berikut : ▪️ ^(a^n) log b^m = m/n ^a log b ▪️ ^a log b . ^b log c = ^a log c ▪️ a^(^a log b) = b ▪️ ^a log a = 1 Penyelesaian : ^(1/5) log√27 ⋅ ^(√(3)) log25 + 9^(^3 log4) = ^(5^(-1)) log(3^(3/2)) ⋅ ^(3^1/2) log(5^2) + (3^2)^(^3 log4) = (3/2)/(-1) ^5 log 3 ⋅ (2/(1/2)) ^3 log 5 + 3^(2⋅ ^3 log 4) = (-3/2)(4) ^5 log 3 ⋅ ^3 log 5 + 3^(^3 log 4^2) = -6 ⋅ ^5 log 5 + 4^2 = -6 + 16 = 10 Jadi, hasil dari nilai logaritma tersebut adalah 10