Matematika

Pertanyaan

Nilai x yang memenuhi persamaan ³log² x – 4 ³log x – ³log 1 = -3 adalah ....
Nilai x yang memenuhi persamaan ³log² x – 4 ³log x – ³log 1 = -3 adalah ....

1 Jawaban

  • [tex]\LARGE _{}^{3}\textrm{log}^2x-4\cdot_{ }^{3}\textrm{log}x-_{ }^{3}\textrm{log}1 = -3[/tex]
    [tex]\LARGE _{}^{3}\textrm{log}^2x-4\cdot_{ }^{3}\textrm{log}x = -3[/tex]
    [tex]\LARGE _{}^{3}\textrm{log}^2x-4\cdot_{ }^{3}\textrm{log}x +3 = 0[/tex]
    [tex]\LARGE _{ }^{3}\textrm{log}x = u[/tex]
    [tex]\LARGE u^2-4u+3=0[/tex]
    [tex]\LARGE (u-3)(u-1)=0[/tex]
    [tex]\LARGE u=3\vee u=1[/tex]
    [tex]\LARGE _{ }^{3}\textrm{log}x=3 \vee _{ }^{3}\textrm{log}x=1[/tex]
    [tex]\LARGE x=27 \vee x=3[/tex]