Question

log(x+3)+log(x-5)= 2 log 3 find x​

Answer 1

Answer:

The value of x is either 6 or -4

Step-by-step explanation:

$log(x + 3) + log(x - 5) = 2 log(3) \\ \implies log(x + 3)(x - 5) = log(3)^{2} \\ \implies(x + 3)(x - 5) = 9 \\ \implies {x}^{2} - 5x + 3x - 15 = 9 \\ \implies {x}^{2} - 2x - 24 = 0 \\ \implies {x}^{2} + 4x - 6x - 24 = 0 \\ \implies x(x + 4) - 6(x + 4) = 0 \\ \implies(x - 6)(x + 4) = 0$

Now we have

$x - 6 = 0 \\ \implies x = 6$

And

$x + 4 = 0 \\ \implies x = - 4$

Formula used

★log(A) + log(B) = log(A×B)