This expression is equal to log base b of 6. Great work if you found this
logarithm. Now again, I think it's easiest to think about having two logarithms
of base b of 8, and three logarithms of base b of 4. We know that to combine
these three logarithms, or to add them together, we'll need to multiply these
numbers together. So, we can express the addition of these three logarithms as
the logarithm of base b of 6 times 8 times 8. Then we'll have the subtraction
of log base b of 4, three times. When we subtract a logarithm, we really divide
this number into this number. Keep in mind this is only true if the logarithms
have the same base. So when I combine this logarithm with this logarithm, we'll
really just divide 6 times 8 times 8, by 4, and we'll take the log of base b of
that expression. These other two logarithms are still on the end. I notice that
I'm going to have to repeat this process. So, if I take this logarithm with
base b and subtract this logarithm with base b, I'm going to divide by another
4. So, we divide by another 4, and then I still have one more logarithm on the
end. I need to subtract this logarithm of base b of 4 from this logarithm of
base b of this expression. So, I'm simply dividing by another 4. This gives me
a logarithm with one number. Now, I just need to simplify. I know 8 times 8
equals 64; and 4 times 4 times 4 also equals 64. So, these factors simplify to
1, which leaves me with log base b of 6. Our final answer.
