tolong bantu yaa pake cara nilai x yang memenuhi persamaan: [tex] \frac{^{x}log 2 }{ ^{2}logx-4} = -\frac{1}{3} [/tex] adalah....

jawab

misalkan ˣlog 2 = a
maka ²log x = 1/a

[tex] \frac{ ^{x}log\, 2}{^2log\,x - 4} \, = \frac{-1}{3} [/tex]

[tex]\frac{ a}{ \frac{1}{a} - 4} \, = \frac{-1}{3}[/tex]


3a = -1/a + 4 ..}kalikan a
3a² = -1 + 4a
3a²  -  4a + 1= 0
(3a -  1)(a - 1) = 0
a=  1/3  atau a =  1

²log x = 1/a
x = (2)^(1/a)
a = 1/3 → x= (2)³ = 8
a = 1 → x = (2)¹ = 2