Задание 2.1

2.1. Решите уравнение: 1) 4x = 64; 2) 3x = 1 81;
3) 0,62x3 = 1; 4) 10x = 0,001
5) 25x = 23x7; 6) 8x = 16; 7) 0,16x = 5 2;
8) 5x = 25; 9) 0,25x24 = 2x2+1 ;

10) (4 9 ) x1 (27 8 ) x1 = 2 3;

11) 2x 5x = 0,1 (10x1) 5;

12) (4 7 ) 3x7 = (7 4 ) 7x3

13) 36x = ( 1 216 ) 2x;

14) 5x22x = 6x22x ;

15) 3x1 = 6x 2x 3x+1.

Answers

 1) 4x = 64;4x = 43;x = 3;  2) 3x = 1 81;3x = 34;x = 4;  3) 0,62x3 = 1;0,62x3 = 0,60;2x 3 = 0;2x = 3;x = 1,5;  4) 10x = 0,001;10x = 103;x = 3;x = 3;  5) 25x = 23x7;5 x = 3x 7;3x + x = 7 + 5;4x = 12;x = 3  6) 8x = 16; (23) x = 24;23x = 24;3x = 4;x = 4 3  7) 0,16x = 5 2; ( 4 10 ) 2x = 5 2; (2 5 ) 2x = (2 5 ) 1;2x = 1;x = 1 2  8) 5x = 25; (5x) 1 2 = 52;51 2 x = 52;1 2x = 2;x = 4  9) 0,25x24 = 2x2+1 ; (1 4 ) x24 = 2x2+1 ; (22) x24 = 2x2+1 ;22x2+8 = 2x2+1 ; 2x2 + 8 = x2 + 1;x2 + 2x2 = 8 1;3x2 = 7;x2 = 7 3;x = ±7 3;  10)  (4 9 ) x1 (27 8 ) x1 = 2 3; (4 9 27 8 ) x1 = 2 3; (3 2 ) x1 = 2 3; (2 3 ) 1x = 2 3; 1 x = 1;x = 0;  11) 2x 5x = 0,1 (10x1) 5;(2 5)x = 101 105x5;10x = 105x6; x = 5x 6;4x = 6;x = 1,5;  12)  (4 7 ) 3x7 = (7 4 ) 7x3; (4 7 ) 3x7 = (4 7 ) 37x;3x 7 = 3 7x;10x = 10;x = 1;  13) 36x = ( 1 216 ) 2x;62x = (63) 2x;62x = 63x6;2x = 3x 6;x = 6;  14) 5x22x = 6x22x ; (5 6 ) x22x = 1; (5 6 ) x22x = (5 6 ) 0;x2 2x = 0;x 1 = 0,x2 = 2;  15) 3x1 = 6x 2x 3x+1;3x1 = 3x 2x 2x 3x+1;3x1 = 20 3x+x+1; 3x1 = 32x+1;x 1 = 2x + 1;x = 2

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2021-12-30 07:13
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