For any system of logarithms we can use the relation: log (a) b = log(x) a / log(x) b where x can be any positive number to be use as the base.

Now using x= 2,

log (8) 256 = log(2) 256 / log(2) 8.

But we know that log(2) 8 =3

Also log (2) 256 = 8

So log(2) 256 / log(2) 8 = 8/3

Or log(2) x = 8/3

Raising both sides to the power 2, we get

x = 2^(8/3)

**Therefore x = 2^(8/3)**

Given:

log(2)*x = log(8)*256

==> log(2)*x = log(2^3)*256

==> log(2)*x = 3*log(2)*256

==> log(2)*x = log(2)*768

Dividing both sides of equation by log(2):

x = 768

Answer:

x = 768

log(2) x = log(8) 256.

To solve for x:

We write log(8) 256 = log(2) 256/log(2) 8 = {log (2) 256}/log(2) 8 = (1/3)log(2) 256 = log (256)^(1/3).

Therefore the given equation becomes:

log(2) x = log(2)* 256(1/3) =

x = 256 ^(1/3) = 6.3496 approximately.

log(2)x=log(8)256

log2 +logX=log8+log 256

log2+log x=log2^3+log2^8

log2+logx=3log2+8log2

logx=3log2+8log2-log2

logx=10log2

logx=log2^10

So x= 2^10=1024