A^(m+n) = (a^m) * (a^n) ;a^(m-n) = (a^m) / (a^n) ; (a^m)^n = a^(m*n) ;
a^(-m) =1/ a^(m) ; a ^0 =1, при всех a ≠ 0 ;
a^x=b^x⇔(a/b)^x =1⇔(a/b)^x =(a/b)^0⇒x =0 .
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а) 3^(x-2) =(1/2)^(2 - x) ; * * * 1/2 =2^(-1) * * *
3^(x-2) =(2^(-1)) ^(2 - x) ;
3^(x-2) =2^ ((-1)*(2 - x) ;
3^(x-2) =2^(x - 2) ; * * * сразу ⇒ x-2 =0 * * *
(3/2)^(x-2) =1;
(3/2)^(x-2) =(3/2)^0 ;
x-2 =0⇒x =2.
б) 4^(x-1) =5^(1-x) * * * (1/5) ^(-1) =1:(1/5)^(1)=1:(1/5)= 5 * * *
4^(x-1) =((1/5)^ (-1))^ (1-x) ;
4^(x-1) =(1/5)^ ( (-1)* (1-x) ) ;
4^(x-1) =(1/5)^ (x-1) ;
x-1 =0⇒ x=1.
в) 2^x+2^(x+1)=3^(x+1)-3^x ;
* * * a^(m+n) =(a^m)*(a^n) например: 2^(3+4) = (2^3) (2^4). *:* * *
2^x+(2^x)*(2^1)=(3^x)*(3^1)-3^x ;
2^x+(2^x)*2=(3^x)*3 -3^x ;
(2^x)*(1+2) =(3^x)*(3 -1);
(2^x)*3 =(3^x)*2; * * *(2^x)/2)*3 =(3^x)⇔(2^x)/2) =(3^x)/3⇔2^(x-1) =3^(x-1)⇒x=1* * *
(2^x)/(3^x) =2/3;
(2/3)^x =2/3;
x=1.