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

1 Answer
MeneerNask
May 16, 2015

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.

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