How do you use the properties of logarithms to rewrite(expand) each logarithmic expression #log(3x^3 y^2)#?

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Answer 1 · 2015-07-06T00:12:56

#log(3x^3y^2) = 3logx + 2logy + log3#

First Property: #log(xy) = logx +logy#

So

#log(3x^3y^2) = log3 + log(x^3) + log(y^2)#

Second Property: #log(x^d) = dlogx#

So

#log(3x^3y^2) = log3 + log(x^3) + log(y^2) = log 3 + 3logx + 2logy#

#log(3x^3y^2) = 3logx + 2logy + log3#