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$\displaystyle \left \{ {{log^3_4y^{ \frac{1}{3}}- \frac{1}{3}^{-3x} =-9} \atop {log^2_4y+ \frac{1}{3}^{-x}*log_4y^3=27-9^{x+1}}} \right.$

Task/27147149
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{ (1/3)?*(Log?y)? -(3?)? = — 9 , { Log?y)? — (3???)? = — 9*27 ,
{ (Log? y)? +3?*3*Log? y = 27 - 9???; ?{ (Log? y)? +(3???)*Log? y = 27 -  (3???)?  ;?
Замена: u = Log? y, v =3??? > 0
{ u? -v? = -9*27 , {(u — v)(u? +uv +v?) = — 9*27 ,
{u? +uv +v? =27 ; ? { u? +uv +v?  = 27 ; ?

{ u — v= — 9 , { u -v = -9 , { u — v = - 9 ,   * * * { u+(-v )= - 9 ,* * *
{ u? +uv +v? =27; ? {(u -v)? +3uv =27;? { uv = -18. ?  * * *{u*(-v) = 18 ; * * *
* * * t? — 9t +18 =0 * * *
{ u = v - 9  ,    { u = v -9 ,
{ (v -9) v = -18 ;  ?{ v? -9v +18 =0 ;

v? — 9v +18 =0  ? v? =3 ,v?= 6
u? = — 6, u? = — 3 .

{3??? =3,   { x =0 ,
{Log? y = -6 ; ? {y = 1/ 2?? ;
или
{3??? =6,    { x =Log?? ,
{Log? y = — 3 ; ?  {y = 1/ 2?  .