Tentukan nilai x dari persamaan di bawah
[tex]\displaystyle 100x^{\log x-2}+x^{2-\log x}-20=0[/tex]
[tex]\displaystyle 100x^{\log x-2}+x^{2-\log x}-20=0[/tex]
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EKSPONEN
LOGARITMA
misal :
x^(log x - 2) = a
100x^(log x - 2) + x^(2 - log x) - 20 = 0
100a + 1/a - 20 = 0
100a² - 20a + 1 = 0
(10a - 1)² = 0
a = 1/10
x^(log x - 2) = 10^(-1)
(log x - 2) log x = -1
(log² x - 2 log x + 1) = 0
(log x - 1)² = 0
log x = 1
x = 10