Solve for x. Round to the nearest thousandth if necessary.

Question

log₂ x + log₂ (x-2) = 3

Answer 1

log (x(x-2) = 3

 

Raising to the power base 2

 

x(x-2) = 2^3

 

x^2 - 2x = 8

 

x^2 - 2x - 8 = 0

 

(x    -  4)(x  +    2) = 0

 

x-4 = 0   x+2 = 0

 

x=4  or x = -2

 

The solution x = -2 is disqualified

and rejected because the log of

a negative number is undefined.

 

check:

 

log 4 + log 2 = 2 + 1 = 3