How do you use the properties of logarithms to rewrite(expand) each logarithmic expression #log_2 ((x^5)/ (y^3 z^4))#?

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Answer 1 · 2015-07-05T22:03:01

#log_2(x^5/(y^3z^4)) = 5log _2x -3log_2y – 4log_2z#

First Property:

#log_b(x/y)=log_b x-log_b y#

So

#log_2(x^5/(y^3z^4)) = log _2(x^5) -log_2(y^3z^4)#

Second Property:

#log_b(x y)=log_b x+log_b y#

So

#log_2(x^5/(y^3z^4)) = log _2(x^5) –(log_2(y^3) +log_2(z^4))#

#= log _2(x^5) –log_2(y^3) –log_2(z^4)#

Third Property:

#log_bx^r=rlog_b x#

So

#log_2(x^5/(y^3z^4)) = log _2(x^5) –log_2(y^3) –log_2(z^4)#

#log_2(x^5/(y^3z^4)) = 5log _2x –3log_2y –4log_2z#