Question

Conseguem ajudar com a resolução?

Resolva as equações:
a. log2(2x - 7) = -2
b. log2 (log2(3x - 61)) = 0
c. log2( log2( log2( log2x))) = 0

Answer 1

Oi Bia

a) 

log2(2x - 7) = -2 

log(2x - 7) = -2log(2)

log(2x - 7) = log(1/4)

2x - 7 = 1/4

8x - 28 = 1
8x = 29
x = 29/8 

b) 

log2(log2(3x - 61))) = 0

log2(3x - 61) = 1 = log2(2)

3x - 61 = 2
3x = 63
x = 21

c)

log2(log2(log2(log10(2x)))) = 0

log2(log2(log10(2x))) = 1

log2(log10(2x)) = 2 = log2(4)

log10(2x) = 4 

2x = 10^4 

x = 5000

.