caluclate log8 (4).

We'll interchange the base and argument and we'll
get:

log8 (4) = 1/log4 (8)

But
8 = 4*2

log8 (4) = 1/log4
(4*2)

We'll use the product property of
logarithms:

log4 (4*2) = log4 (4) + log4 (2) = 1 + log4
(2)

But log4 (2) = 1/log2 (4) = 1/log2
(2^2)

We'll use the power property of logarithms and log2
(2) = 1

1/log2 (2^2) = 1/2log2 (2) =
1/2

1/log4 (4*2) = 1/[1 + log4 (2)] = 1/(1 + 1/2) =
1/[(2+1)/2] = 1/(3/2) = 2/3

Therefore, the
requested value for log8 (4) = 2/3.