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

Marcus Frank

Marcus Frank

Answered question

2022-12-24

How to rewrite (expand) each logarithmic expression using the characteristics of logarithms log2(x5y3z4)?

Answer & Explanation

eyakhiwabhn

eyakhiwabhn

Beginner2022-12-25Added 6 answers

1 Property:
logb(xy)=logbxlogby
So
log2(x5y3z4)=log2(x5)log2(y3z4)
2 Property:
logb(xy)=logbx+logby
So
log2(x5y3z4)=log2(x5)(log2(y3)+log2(z4))
=log2(x5)log2(y3)log2(z4)
3 Property:
logbxr=rlogbx
So
log2(x5y3z4)=log2(x5)log2(y3)log2(z4)
log2(x5y3z4)=5log2x3log2y4log2z

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