РЕШИТЕ ТРИ ПОКАЗАТЕЛЬНЫХ УРАВНЕНИЯ. Created by DomnikaMaksimova. algebra-ru

РЕШИТЕ ТРИ ПОКАЗАТЕЛЬНЫХ УРАВНЕНИЯ...

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DomnikaMaksimova СПАСИБО БОЛЬШОЕ .))

oganesbagoyan

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A^x =b^x * * * a >0 , b>0 ,a≠b * * *
(a/b)^x= 1⇔(a/b)^x= (a/b)⁰ ⇒ x=0.
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1) (2²)^(x-3) =(3²)^(x-3) ;
4^(x-3) =9^(x-3) ;
x-3 = 0;
x=3 .
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2) 5^(x-2) = 4^(2x -4) ;
5^(x-2) = 4^2(x -2) ;
5^(x-2) = (4²)^(x -2) ;
5^(x-2) = 16^(x -2) ;
x-2 =0 ;
x =2.
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3) 9 ^(-√(x -1) ) = 1/27 ;
(3²) ^ (-√(x -1) ) =3 ^(-3) ;
3 ^(-2√(x -1) ) = 3 ^(-3) ;
-2√(x -1) = -3 ;
√(x -1) =3/2 ;
x -1 =(3/2)² ;
x =1+2,25 ;
x =3,25.

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