Question

How do you use the properties of logarithms to rewrite and simplify the logarithmic expression of `2log8^4-1/3log8^8`?

Answer 1

First you may put all exponents in the log-argument in front of the log:

`=4*2log8-8*1/3log8` then we can combine:

`=(8-8/3)log8=16/3log8`

If we consider that `8=2^3` we can take this exponent out as well:

`=16/3 log2^3=3*16/3log2=16log2`

Of course you could do the `2^3` thing first. The order of operations does not really matter.