Question

Tentukan nilai x dari persamaan di bawah
[tex]\displaystyle 100x^{\log x-2}+x^{2-\log x}-20=0[/tex]

Answer 1

Verified answer

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