Question

Calcule o valor de x nas equações:
a)log4 (2x-3) = 1
b)logx (2x+3) = 2
c)log (10x-1) = log (x+17)

Answer 1

a)

$log_4\ (2x-3)=1\\\\ 4^1=2x-3\\\\ 4=2x-3\\\\ 2x=4+3\\\\ 2x=7\\\\ \boxed{x=\frac{7}{2}}$

b)

$log_x\ (2x+3)=2\\\\ x^2=2x+3\\\\ x^2-2x-3=0\\\\ \Delta=4+12\\\\ \Delta=16\\\\ x'=\frac{2+4}{2}=\frac{6}{2}=3\\ x''=\frac{2-4}{2}=\frac{-2}{2}=-1\\\\ \boxed{S(3)}$

Negativo não entra na solução.

c) 

$log\ (10x-1)=log\ (x+17)\\\\ 10x-1=x+17\\\\ 10x-x=17+1\\\\ 9x=18\\\\ x=\frac{18}{9}\\\\ \boxed{x=2}$