We have to find the value of log(8)4.
Let log(8) 4 = x
=> 4 = 8^x
=> 2^2 = 2^3^x
=> 2^2 = 2^3x
As the base is the same, we equate the exponent
=> 3x = 2
=> x = 2/3
The required value is log(8) 4 = 2/3
We need to find the values of log8 (4)
We will use logarithm properties to solve.
We know that:
loga b = logc b/ logc a
Then we will rewrite:
log8 4 = log2 4 / log2 8
Now we will simplify:
==> log8 4 = log2 2^2 / log2 2^3
==> log8 4 = 2log2 2 / 3log2 2
But log2 2 = 1
==> log8 4 = 2/3