Question

Log^2(3)x - log(3)x = 6

Answer 1

.
$\log^2_3x-\log_3x=6$

vamos colocar

$\log_3x=y \\ \\ y^2-y=6 \\ y^2-y-6=0$

Δ=b²-4ac
Δ=(-1)²-4(1)(-6)
Δ=1+24
Δ=25

y=(-b±√Δ)/2a

y=1±√25)/2a

y=(1±5)/2

y'=(1+5)/2=6/2=3

y"=(1-5)/2=-4/2=-2  (n/ serve)

como

$\log_3x=y \\ \\ \log_3x=3 \\ \\ x=3^3 \\ \\ x=27$