Matematika (+50) KuMat - Kuis Matematika Materi: Logaritma Diketahui: [tex]\large\text{$\begin{aligned}&{}^{\sf2}\log\left({}^{\sf8}\log x\right)={}^{\sf8}\log\left({}^{\sf2}\log x\right)\end{aligned}$}[/tex] Pertanyaan: [tex]\Large\text{$\begin{aligned}&\left({}^{2}\log{x}\right)^2=.....?\end{aligned}$}[/tex]

daphneedenesikulv – June 09, 2023

(+50) KuMat - Kuis Matematika
Materi: Logaritma

Diketahui:
[tex]\large\text{$\begin{aligned}&{}^{\sf2}\log\left({}^{\sf8}\log x\right)={}^{\sf8}\log\left({}^{\sf2}\log x\right)\end{aligned}$}[/tex]

Pertanyaan:
[tex]\Large\text{$\begin{aligned}&\left({}^{2}\log{x}\right)^2=.....?\end{aligned}$}[/tex]

Jawaban:

[tex]\Large\text{$\begin{aligned}&\left({}^{2}\log{x}\right)^2=27\end{aligned}$}[/tex]

Penjelasan dengan langkah-langkah:

²log(⁸log x) = ⁸log (²log x)

²log(²^³log x) = ²^³log(²log x)

²log(²logx⅓) = ²log(²log x)⅓

²log x⅓ = (²log x)⅓

misal, ²log x = a

maka,

²log x⅓ = (²log x)⅓

⅓ ²log x = (²log x)⅓

⅓a = a⅓

1/27a³ = a

1/27a² = 1

a² = 27

(²log x)² = 27

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