Question

log(x+4) + log(x-4)=log 3​

Answer 1

Answer:

x=√19

Step-by-step explanation:

log(x+4)+log(x-4)=log3

we know that log m + log n=log mn

so log (x+4)(x-4)=log 3

so (x+4)(x-4)=3

    x²-16=3

    x²=19

    x=√19

Answer 2

Step-by-step explanation:

$log(x + 4) + log(x - 4) = log(3) \\ \\ log((x + 4)(x - 4)) = log(3) \\ \\ \because \: log((a \times b)) = log(a) + log(b)$

taking antilog both sides

$(x + 4)(x - 4) = 3 \\ \\ {x}^{2} - 16 = 3 \\ \\ \because \: (x - y)(x + y) = {x}^{2} - {y}^{2} \\ \\ {x}^{2} = 3 + 16 \\ \\ {x}^{2} = 19 \\ \\ x = ± \sqrt{19}$

Hope it helps you.