Question

1. Resolva, em R, cada equação.
a) log(5-2x)=log(2x-11)
b) 2.log x=log x +log (5x-4)
c) [loga+1(x)}- loga+1(x)=6
d) logo,5(x²+3x)=-2 =-2
e) 4-loge+1(x)+4-log (2+1)=17​

Answer 1

Explicação passo-a-passo:

a) log(5-2x)=log(2x-11)

log 2x-11(5-2x)= 1

5-2x= 2x-11

4x=16

x= 4

b) 2.log x=log x +log (5x-4)

logx²= log(5x²-4x)

log x² (5x²-4x)= 1

5x²-4x= x²

4x²= 4x

x= 1

c) [loga+1(x)}- loga+1(x)=6

log a+1( x²)= 6

x²= (a+1)^6

x=(a+1)³

x=(a²+2a+1)(a+1)

x= a³+3a²+3a+1

d) logo5(x²+3x)=-2

x²+3x= 5-²

x²+3x= 1/25

x²+3x -1/25=0

x= -3±√( 9+4/25)/2

x= -15+√229/10

x≈ 0,0132

e) 4-loge+1(x)+4-log (2+1)=17

"-loge+1(x)" verifique se esse log estar correto