Solve the system of equations Log3x=2log3y=1; X+3y²=54 (Log3x equally 2 logarithm of 3y equally 1; X plus 3y squared equally 54) several equations [THERE'S THE ANSWER!] online

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log(3*x) = 2*log(3*y)

$$\log{\left(3 x \right)} = 2 \log{\left(3 y \right)}$$

       2     
x + 3*y  = 54

$$x + 3 y^{2} = 54$$

x + 3*y^2 = 54

Rapid solution

$$x_{1} = 27$$
=
$$27$$
=

$$y_{1} = 3$$
=
$$3$$
=

Numerical answer [src]

x1 = 27.0 + 5.0324007822766e-20*i
y1 = 3.0 + 1.070582417132303e-20*i

x2 = 27.0 + 3.966987995042471e-30*i
y2 = 3.0 - 1.084715367979446e-31*i

x3 = 27.0 - 3.384852807742659e-37*i
y3 = 3.0 + 2.095389619674185e-40*i

x4 = 27.0 + 5.557859376943305e-29*i
y4 = 3.0 - 7.963614621334069e-30*i

x5 = 27.0
y5 = 3.0

x6 = 27.0 + 7.119523105047169e-25*i
y6 = 3.0 + 3.20067101569518e-27*i

x6 = 27.0 + 7.119523105047169e-25*i
y6 = 3.0 + 3.20067101569518e-27*i

Log3x=2log3y=1; X+3y^2=54