Find the exact solution or solutions of the equation

Question

2log7 √6x-2 -log7(x+1)=0

 

note: the 7 is the basis for log 

Answer 1

2log₇√(6x-2) - log₇(x+1) = 0

 

log₇ (6x-2) - log₇(x+1) = 0

 

log₇[(6x-2)/(x+1)] = 0

 

(6x-2)/(x+1) = 7⁰

 

6x-2 = x+1

 

    5x = 3

 

     x = 3/5

 

Answer 2

2log(7)√(6x-2)-log(7)(x+1)=0

log(7)(√(6x-2))²-log(7)(x+1)=0

log(7)[(√(6x-2)²)/(x+1)]=0

log(7)[(6x-2)/(x+1)]=0

7⁰=(6x-2)/(x+1)

7⁰=1

1=(6x-2)/(x+1)

x+1=6x-2

1+2=6x-x

3=5x

x=3/5