Write as the sum and\or difference of logarithms. Express powers as factors. \log_{2}(\frac{xy^{4}}{z^{5}})

pancha3

pancha3

Answered question

2021-08-09

Write as the sum and/or difference of logarithms. Express powers as factors. 
log2(xy4z5)

Answer & Explanation

Jayden-James Duffy

Jayden-James Duffy

Skilled2021-08-10Added 91 answers

Given log2(xy4z5) 
Here we write as the sum and/or difference of logarithms. 
Now log2(xy4z5) 
=log2(xy4)log2(z5) 
=(log2x+log2y4)log2(z5)[loga(mn)=logam+logan] 
=log2x+4log2y5log2z[lognxm=mlogax] 
Hence log2(xy4z5)=log2x+4log2y5log22

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