Question

the solution set of log2(3-x) +log2(1-x)=3 is

Answer 1

EXPLANATION.

Solutions of the set.

⇒ ㏒₂(3 - x) + ㏒₂(1 - x) = 3.

As we know that,

Formula of :

⇒ ㏒ₐM + ㏒ₐN = ㏒ₐMN.

Using this formula in the equation, we get.

⇒ ㏒₂(3 - x)(1 - x) = 3.

⇒ (3 - x)(1 - x) = 2³.

⇒ 3 - 3x - x + x² = 8.

⇒ x² - 4x + 3 = 8.

⇒ x² - 4x + 3 - 8 = 0.

⇒ x² - 4x - 5 = 0.

Factorizes the equation into middle term splits, we get.

⇒ x² - 5x + x - 5 = 0.

⇒ x(x - 5) + 1(x - 5) = 0.

⇒ (x + 1)(x - 5) = 0.

⇒ x = - 1 and x = 5.

As we know that,

⇒ ㏒ₐ(x) = a > 0.

∴ only one solution exists.