Solve for x the equation log2(x)=log2(4)+3logx(2)

We'll write log2 (4) = log2
(2^2)

We'll apply the power
property:

log2 (2^2) = 2*log2
(2)

But log2 (2) = 1 => log2 (4) =
2

We'll write log(x) 8 = 1/log (8)
x

log(2) x =log(8) x*log(2)
8

log(2) 8= log(2) (2^3)

We'll
use the power property of logarithms:

log(2) (2^3) =
3log(2) (2) = 3

log(2) x =3*log(8) x => log(8)
x=log(2) x/3

The equation will
become:

log(2) x - 2 - 3/log(2) x =
0

[log(2) x]^2 - 2log(2) x - 3 =
0

Let log(2) x be t:

t^2 - 2t
- 3 = 0

t1 = [2+sqrt(4 +
12)]/2

t1 = (2+4)/2

t1 =
3

t2 = -1

log(2) x = 3
=> x = 2^3 => x = 8

log(2) x = -1 => x
= 2^-1 => x = 1/2

The requested
solutions of the equation are: x = 1/2 and x = 8.