Question

Resolver las siguientes ecuaciones​

Answer 1

Respuesta:

a) x = 1 ; x = 2

b) x = 4096

Explicación paso a paso:

a) 4^(x) + 8 = 3(2)^(x+1)

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

(2^(x))^2 + 2^(3) = 3 . (2)^(x) . 2^(1)

2^(x) = a

-----

(a)^(2) + 2^(3) = 3 . a . 2^(1)

a^(2) + 8 = 6a

a^(2) - 6a + 8 = 0

( a - 4 ) ( a - 2) = 0

a = 4 ; a = 2

-----

2^(x) = a

2^(x) = 4

x = 2

----

2^(x) = a

2^(x) = 2

x = 1

------------

b)

log 4 (x) + log 16 (x) = 9

log 4 (x) + log 4² (x) = 9

(1) log 4 (x) + (1/2) log 4(x) = 9

(1 + 1/2) log 4(x) = 9

(3/2) log 4(x) = 9

3log 4(x) = 2(9)

3log 4(x) = 18

log 4(x) = 18/3

log 4(x) = 6

x = 4⁶

x = 4096