Solve and show work please

Question

log₄ 6 + log₄ (x + 2) = 2

Answer 1

First, condense the logs on the left side of the equation.

 

log₄(6(x + 4)) = log₄2

 

 

Next, equate the arguments of logs.

 

6(x + 4) = 2

 

 

Solve for x.

Answer 2

log₄6 + log₄(x + 2) = 2

 

log₄[6(x + 2)] = 2

 

Take 4⁽⁾ on both sides.

 

6(x + 2) = 4² = 16

 

6x + 12 = 16

 

x = (16 - 12)/6 = 4/6 = 2/3

 

x = 2/3

Answer 3

Using the property log(a) + log(b) = log(ab), the left hand side can be re-written: 

 

log₄(6*(x+2)) = 2     

 

Now raise 4 to both sides:

    6(x+2) = 4²

   

Solve for x and you are done.