3^(2Loq(3) 6) = 3^(Loq(3) 6² ) =6² =36.
----------------------
(27^(1/2 *(1/9)^3/4) ^(4/3) =(3^(3/2) *(1/3)^(2*3/4))^(4/3) =((3*1/3)^(3/2))^(4/3) =1^(4/3) =1.
----------------------
Loq(2) (2x+1) =3;
2x+1 =2³ ;
2x =7 ;
x =3,5.
---------------
7^(x+1) -14*7^x =5;
7*7^x -14*7^x =5 ;
-7*7^x =5 ;
7^x = -5/7 _не имеет решения
**********************
7^(x+2) -14*7^x =5;
7²*7^x -14*7^x =5 ;
7^x *(49-14) =5 ;
7^x =5/35 ;
7^x =1/7 ;
7^x =7^(-1) ;
x= -1
----------------------
100^ (2x+1) =1/10 ;
10^(2*(2x+1)) =10 ^(-1) ;
2*(2x+1) = -1 ;
2x+1 = -1/2 ;
2x = -3/2 ;
x = - 3/4 .
--------------------
интеграл( 4x^3 -5x +x² -7)dx = 4*(x^4)/4 -5*x²/2 +x³/3 -7x +C =
= x^4 +x³/3 -5x²/2 -7x+C.