Question

rozwiązywanie równan wykladniczych prosze o pomoc

Answer 1

z.716

a)  4^x * 2^x = 64

(2 ^2)^x * 2^x = 2^6

2^(2x) *2^x = 2^6

2^(2x + x) = 2^6

3x = 6

x = 2

=====

b)

0,25 ^x * 8^(x -1) = 2

(1/4)^x * ( 2^3)^(x -1) = 2

[(1/2)^2]^x  * 2^(3x) = 2

(1/2)^(2x)  * 2^(3x) = 2

[ 2 ^(-1)]^(2x) * 2^(3x) = 2

2^(-2x) * 2^(3x) = 2

2^(-2x +3x) = 2

2^x = 2

x = 1

======

c)

10^x *100^x *1000^x = 0,1^(1 -x)

10^x * (10^2)^x * (10^3)^x = [(10^(-1)]^(1 -x)

10^x * 10^(2x) * 10^(3x) = 10 ^(x -1)

10^(x +2x +3x) = 10^(x -1)

10^(6x) = 10^(x -1)

6x = x - 1

5x = - 1

x = -1/5

=============

d)

[ p(2)]^x * [ p(8)]^x = 32

[ p(2)]^x * [ p(2)^3]^x = 32

[ p(2)]^x * [ p(2)]^3x = 32

[ p(2)]^(4x) = 32

[ (p(2)^2]^(2x) = 2^5

2^(2x) = 2^5

2x = 5

x = 2,5

==========

e)

[ 10 p(1000)]^x * 0,1^x = [ p5st(0,1)]^(3x + 2)

[ 10 * 10 p(10)]^x * 0,1 ^x = [ 0,1^(1/5)]^(3x + 2)

[100 * 10^(1/2)]^x * [ 10^(-1)]^x = [ (10^(-1)) ^(1/5)]^(3x + 2)

[ 10^2 * 10^(1/2)]^x * 10^(-x) = [ 10^(-1/5)]^(3x + 2)

[10^2,5]^x * 10^(-x) = 10 ^(-0,6x - 0,4)

10^2,5x * 10^(-x) = 10 ^( -0,6x - 0,4)

10^(1,5x) = 10^( -0,6 x - 0,4)

1,5x = -0,6x - 0,4

2,1 x = - 0,4

21x = - 4

x = - 4/21

===========

f)

7^x *(1/49)^(2x) = 7* [ p3st(7)/7]^x

7^x *( 7^(-2)]^(2x) = 7*[ 7^(1/3) / 7]^x

7^x * 7^(-4x) = 7*[ 7^(-2/3)]^x

7^(-3x) = 7*7^[( -2/3) x]

7^(-3x) = 7^[ (-2/3) x + 1]

-3x = (-2/3)x + 1

( -7/3) x = 1

x = - 3/7

===========

 z.717

a)

2^x + 2^(x +2) = 20

2^x + 2^2 * 2^x = 20

2^x +4 *2^x = 20

5* 2^x = 20  / : 5

2^x = 4

x = 2

========

b)

3^x - 3^(x-1) = 54

3^x - (1/3)*3^x = 54

(2/3)* 3^x = 54  / * 3/2

3^x = 81

3^x = 3^4

x = 4

================

c)

10^(2x + 1) - 10^(2x -1) =990 p(10)

10^10^(2x) - (1/10)*10^(2x) = 990 p(10)

9,9 *10^(2x) = 990 p(10)   / : 9,9

10^(2x) = 100 p(10)

10^(2x ) = 10^2 * 10^(1/2)

10^(2x) = 10^2,5

2x =2,5

x = 1,25 = 5/4

=================

 d)

9^(x/2) + 3^(x +2) = p( 2 700)

(3^2)^(x/2) + 3^2 * 3^x = p( 9*3*100)

3^x +9* 3^x = 3*10*p(3)

10* 3^x = 10* 3^1 * 3^(1/2)  / : 10

3^x = 3^(1,5)

x =1,5

===================

e)

5^(2x) + 25^(x +1) = 1,04

(5^2)^x + 25 *25^x = 1  1/25

25^x + 25 *25^x = 26/25

26* 25^x = 26/25   / : 26

25^x - 1/ 25

25^x = 25^(-1)

x = - 1

====================

f)

1/( 7^x) + 7^(2 - x) - 350

7^(-x) + 7^2 * 7^(-x) = 350

7^(-x) + 49 *7^(-x) = 350

50 * 7^(-x) = 350  / : 50

7^(-x) = 7

-x = 1

x = - 1

===============