Question

Como se resolve?
log3(x) + log x(3) = -2

Answer 1

Ola Tata

log3(x) + logx(3) = -2

log(x)/log(3) + log(3)/log(x) = -2

log²(x) + log²(3) = -2*log(3)*log(x) 

log²(x) + 2log(3)log(x) + log²(3) = 0

y = log(x)

y² + 2log(3)y + log²(3) = 0

delta
d² = 4log²(3) - 4log²(3) = 0
d = 0

y = -2log(3)/2 = -log(3)

y = log(x)

log(x) = -log(3)

x = 1/3