1.) Jika ²㏒ 3 = a dan ³㏒ 5 = b, nilai dari ¹⁸㏒ 50 = .... 2.) Jika a = 0,9090..... dan b = 1,331, maka a ㏒ b =.... Tolong dilengkapi caranya :)

jawab

1.
²log 3 = a
³log 5 = b 

(²log 3. ³log 5) =  ab
²log 5 = ab


¹⁸log50 = ²log 50 /²log 18
= (²log 2 + ²log 5²)/(²log 2 +²log 3²)
= ( 1 + 2. ²log 5) / (1 + 2. ²log 3)
=  ( 1+ 2 ab )/ (1 + 2a)


2)
a= 0,9090
100a = 90,90
99a = 90
a = 90/99
a= 10/11

b = 1,331 = 1,1³

ᵃlog b = ¹°/¹¹log (11/10)³ = ¹°/¹¹ log (10/11)⁻³ = - 3

1.) Gunakan sifat logaritma
[tex] {}^{a} log(b) = \frac{ {}^{x}logb }{ {}^{x} loga} \\ \\ {}^{18} log(50) = \frac{ {}^{2} log(50) }{ {}^{2} log(18) } \\ = \frac{ {}^{2} log(2) \times 5 {}^{2} }{ {}^{2} log(2) \times 3 {}^{2} } \\ = \frac{ {}^{2} log(2) + {}^{2} log(5) + {}^{2} log(5) }{ {}^{2} log(2) + {}^{2} log(3) + {}^{2} log(3) } \\ = \frac{1 + 2ab}{1 + 2a} [/tex]

2.) a = 0,9090 → 10 / 11
b = 1,331 → (11/10)³

Maka

[tex] {}^{a} log(b) = {}^{ \frac{10}{11} } log( \frac{11}{10} ) {}^{3} \\ = {}^{ \frac{10}{11} } log( \frac{11}{10} ) {}^{ - 3} \\ = 3. {}^{ \frac{10}{11} } log( \frac{11}{10} ) \\ = - 3[/tex]