Question

find the value of x for wich ㏒₂2x + ㏒₂(x+4) = 6

Answer 1

(2x / x+4) =64
2x=64x +256
-62x =256
x=4.27

Answer 2

We know the property, logx + logy = logxy

then,

l
$log_{2}({2x} \times x + 4)$= 6

so,

taking anti log on both side,

2x (x+4) = 2^6
2x^2 + 8x = 2^6
2x^2 + 8x - 2^6 = 0
2x^2 + 8x - 64 = 0
2x^2 + 16x - 8x - 64 =0
2x (x + 8) -8 (x+8) =0
(2x-8)(x+8) =0

so, x = 4,-8

hope this helps you out!