Question

Resolva as equações:

a) $log(x + 4) = 0$

b) $log_{2}(x + 3) + log_{2}(x - 4)= 3$

c) $log_{2}(4) + log_{2}(x) = 3$

d) $2 log(x)=log(1000)+ log(10)$

e) $log( \sqrt{x} ) + log_{100}(x) = 2$

Answer 1

1)

log (x + 4) = 0

 x + 4 = 10^0
 x + 4 = 1
 x = - 3

2)

log(2) (x + 3) + log(2) (x - 4) = 3
log(2) [(x + 3)(x - 4)} = 3
(x + 3)(x - 4) = 3
x² - 12 = 3
x² = 15
x = 5

3) 

log(2) (4) + log(2) (x) = 3
log(2) (4x) = 3
4x = 2³
4x = 8
x = 2



4)  2log(x) = log (1000) + log(10)
     log(x)² = 3 + 1
     log x² = 4
      x² = 10^4
      x = √10^4
      x = 10² ⇒ 100



5) log(√x) + log(100) (x) = 2
    log(√x) + log(10²) (x) = 2
   1/2log (x) + 1/2log (x) = 2
    log (x . x)/2 = 2
    log x² = 4
    x² = 10^4
    x = √10^4
   x = 10²