Решите уравнения 1) (1/13)^(2x+9) = 13^х 2) (1/30)^(х-3/5) = 30^х 3) (1/3)^(-3х-16) =...

Question

Решите уравнения
1) (1/13)^(2x+9) = 13^х

2) (1/30)^(х-3/5) = 30^х

3) (1/3)^(-3х-16) = 243^х

4) 49^(2х-3) = 1/7

5) 0,25^(8-5х) = 1/0,125

Answer 1

( 1/13 ) ^ ( 2x + 9 ) = 13 ^ x 
13 ^ ( - 2x - 9 ) = 13 ^ x 
- 2x - 9 = x 
3x = - 9 
x = - 3 
------------------
( 1/30 ) ^ ( x - 3/5 ) = 30 ^ x 
30 ^ ( - x + 3/5 ) = 30 ^ x 
- x + 3/5 = x 
2x = 3/5 
x = 0,3 
----------------------
( 1/3 ) ^ ( - 3x - 16 ) = 243 ^ x 
3 ^ ( 3x + 16 ) = 3 ^ 5
3x + 16 = 5 
3x = - 11 
x = - 11/3 
x = - 3 2/3 
-----------------------
49 ^ ( 2x - 3 ) = 1/7 
7 ^ ( 4x - 6 ) = 7 ^ ( - 1 ) 
4x - 6 = - 1 
4x = 5 
x = 1,25 
-----------------------
0,25 ^ ( 8 - 5x ) = 1 / 0,125 
( 1/4 ) ^ ( 8 - 5x ) = 8 
( 2 ^ ( - 2( 8 - 5x )) = 2 ^ 3 
- 2( 8 - 5x ) = 3 
- 16 + 10x = 3 
10x = 19 
x = 1,9

Comments

Спасибо большое