Question

log5 (x - 3) + log5 (x + 4) = log5 8​

Answer 1

EXPLANATION.

⇒ ㏒₅(x - 3) + ㏒₅(x + 4) = ㏒₅(8).

As we know that,

Formula of :

⇒ ㏒ₐM + ㏒ₐN = ㏒ₐ(MN).

Using this formula in the equation, we get.

⇒ (x - 3)(x + 4) = 8.

⇒ x² + 4x - 3x - 12 = 8.

⇒ x² + x - 20 = 0.

Factorizes this equation into middle term splits, we get.

⇒ x² + 5x - 4x - 20 = 0.

⇒ x(x + 5) - 4(x + 5) = 0.

⇒ (x - 4)(x + 5) = 0.

⇒ x = 4   and   x = - 5.

As we know that,

⇒ ㏒ₐ(x) > 0.

So, value of x = 4.