What are the real solutions of the equation?

log2(x+1)+log2(x-2)=2

Expert Answers

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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.

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