log x²+log y²= 4 log x⁻¹ + log y = 0 mengubahke sistem persamaan linier ?? plisss bntu

log[tex]x^{2}[/tex] + log[tex]y^{2}[/tex] = 4
log[tex]x^{2}y^{2}[/tex] = log[tex]10^{4}[/tex]
[tex]x^{2}y^{2}[/tex] = [tex]10^{4}[/tex]
[tex](xy)^{2}[/tex] = 10000
xy = [tex]\sqrt{10000}[/tex]
xy = 100 ... (1)

log[tex]x^{-1}[/tex] + log y = 0
log[tex]\frac{y}{x}[/tex] = log 1
[tex]\frac{y}{x}[/tex] = 1
y = x ... (2)

persamaan (2) dimasukkan ke persamaan (1), sehingga menghasilkan:
xy = 100
x × x = 100
[tex]x^{2}[/tex] = 100
x = [tex]\sqrt{100}[/tex]
x = 10
berdasarkan persamaan (2), didapat:
y = x = 10
maka: x = 10, y = 10