solve the equation

Question

log2(2x + 2) + log2(x + 5) = log2 10

Answer 1

Use identity:

 

log_ax+log_ay=log_a(xy)

 

Apply this to your equation to get:

 

log₂((2x+2)*(x+5))=log₂10

 

From this it follows that:

 

(x+1)(x+5)=5

x>-1, x>-5

 

The inequalities come from the requirement that the argument of the logarithm function must be positive.

               

x²+6x+5=5 

x>-1

 

x(x+6)=0

x>-1

 

x=0, x=-6

x>-1

 

The only solution is x=0, since -6<-1.

 

Answer: x=0