Respuestas
1. Hallar x en cada caso
a. 8^x = 4^5 * 4^3 * 4^2 / 4^10
2^3x= 4^10 / 4^10
2^3x = 2^0
3x = 0
x = 0
b. x= 2^2 * 2^3 *2^10 / 2^9
x= 2^15/ 2^9
x= 2^6
x= 64
c. (24)2 = (12)2 * 2x
48= 24* 2x
48= 48x
x= 48/48
x= 1
d. 5^x= 5^0 * 5^1 * 5^2 * 5^3 * 5^4/ 5^5
5^x = 1 * 5 * 5^2 * 5^3 * 5^4 / 5^5
5^x = 5^2 * 5^3 * 5 ^4 / 5^4
5^x = 5^2 * 5^3
5^x = 5^5
x = 5
e. 8x= 43
x= 43/ 8
x= 5.375
f. 2x= 102 + 102 - 142
2x = 204 - 142
2x = 62
x = 62/2
x = 31
g. x5 = (18)5 * (6)5
5x = 90 * 30
5x = 2700
x = 2700/5
x = 540
h. x20 = 54 * 56 * 510
20x = 1542240
20x = 1542240/ 20
x = 77112
i. 72x= 73 * 710 * 77
72x = 3990910
x = 3990910 / 72
x = 55429.30
j. 11^x3 = 3^10 * 5^7 * 8 ^3 * 25 / 2^6 * 5^2 * 3^8 * 5 ^7 * 2^3 20^0 1
11^3x = 3^10 * 5^7 * 8^3 * 25 / 2^6 * 5^2 * 3^8 * 5^7 * 2^5
11^3x = 3^10 * 5^7 * 2^9 * 5^2 / 2^6 * 5^2 * 3^8 * 5^7 * 2^5
11^3x = 3^ 10 * 2^9 * 5^2 / 2^6 * 5^2 * 3^8 * 2^5
11^3x = 3^2 * 2^9 * 5^2 / 2^6 * 5^2 * 25
11^3x = 3^2 * 2^9 / 2^6 * 2^5
11^3x= 9 * 2^9 / 2^11
11^3x= 9 * 2^3 / 2^5
11^3x = 9/ 2^2
11^3x= 9 / 4
3x = 2log11 (3/2)
x = 2/3 * log11 (3/2)
x = 0.112
- el " ^ " significa la potencia
- el " / " indica la separacion de la fraccion
- el " * " significa por
2. Reducir en cada caso :
a. E= 7^20 / 7^18 * 4^5 * 4^10/ 4 ^14 * 3^10 * 3^7/ 3^15
E = 7^2 * 4^15/ 4^14 * 3^17/ 3^15
E= 49 * 4 * 3^2
E= 49 * 4 * 9
E= 1764
b. F= (17)2 - (13)2 + 83- 52 + 150
F= 34 - 26 + 83 - 52 + 150
F= 189
c. G= (20027 - 19805)0 + (π)0 + 1
G= ( 222)0 + (π)0 + 1
G = 0 + 0 + 1
G= 1