We have to find the solution of log(2)(x+1) + log(2)(x-2) = 2
log(2)(x+1) + log(2)(x-2) = 2
use log a + log b = log a*b
=> log(2) (x+1)(x-2) = 2
=> (x+1)(x-2) = 2^2
=> x^2 - x - 2 = 4
=> x^2 - x - 6 =...
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Already a member? Log in here.
We have to find the solution of log(2)(x+1) + log(2)(x-2) = 2
log(2)(x+1) + log(2)(x-2) = 2
use log a + log b = log a*b
=> log(2) (x+1)(x-2) = 2
=> (x+1)(x-2) = 2^2
=> x^2 - x - 2 = 4
=> x^2 - x - 6 = 0
=> x^2 - 3x + 2x - 6 = 0
=> x(x - 3) + 2(x - 3) = 0
=> (x + 2)(x - 3) = 0
=> x = -2 and x = 3
As the log of a negative number is not defined eliminate x = -2.
The required solution of the equation is x = 3.