| Certified Educator
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
| Certified Educator
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'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.
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