berapa nilai x yang memenuhi 4 log ( 2 log x ) + 2 log ( 4 log x ) = 2

Mata Pelajaran : Matematika Peminatan
Kelas : 10
Bab : 02 - Fungsi Logaritma




[tex] {}^{4} log( {}^{2} logx) + {}^{2} log( {}^{4} logx) = 2 \\ {}^{2 {}^{2} } log( {}^{2} logx) + {}^{2} log( {}^{4} logx ) = 2 \\ \frac{1}{2} \times {}^{2} log( {}^{2} logx) + {}^{2} log( {}^{4} logx) = 2 \\ \\ kalikan \: kedua \: ruas \: dgn \: 2 \\ sehingga \\ \\ {}^{2} log( {}^{2} logx) + 2. {}^{2} log( {}^{4} logx) = 4 \\ {}^{2} log( {}^{2} logx ) + {}^{2} log( {}^{4} log(x ) {}^{2} ) = 4 \\ {}^{2} log( {}^{2} logx. {}^{4} log(x {} ) {}^{2} ) = 4 \\ {}^{2} log_{}(x) . {}^{4} log(x) {}^{2} = 2 {}^{4} \\ {}^{2} log(x) . {}^{2 {}^{2} } log(x) {}^{2} = 16 \\ {}^{2} log(x) \times ( \frac{1}{2} \times {}^{2} logx) {}^{2} = 16 \\ {}^{2} log(x) . \frac{1}{4} . {}^{2} log(x) {}^{2} = 16 \\ \frac{ {}^{2} log(x) {}^{3} }{4} = 16 \\ {}^{2} log(x) {}^{3} = 64 \\ {}^{2} log(x) = 4 \\ x = 2 {}^{4} \\ x = 16[/tex]