Condense using properties of logarithms: \(\displaystyle{\log{{13}}}+{\frac{{13}}{{\log{{\left({x}-{9}\right)}}}}}–{3}{\log{{\left({x}+{9}\right)}}}\)

burubukuamaw

burubukuamaw

Answered question

2022-03-25

Condense using properties of logarithms: log13+13log(x9)3log(x+9)

Answer & Explanation

Aidyn Wall

Aidyn Wall

Beginner2022-03-26Added 10 answers

Given :
log13+13log(x9)3log(x+9)
Using logab=bloga,
log13+13log(x9)3log(x+9)=log13+log(x9)13log(x+9)3
Using loga+logb=log(ab),
log13+13log(x-9)-3log(x+9)=log(13(x-9)13)-log(x+9)3
Using logalogb=log(ab),
log13+13log(x-9)-3log(x+9)=log(13(x-9)13(x+9)3)
Therefore
log13+13log(x-9)-3log(x+9)=log(13(x-9)13(x+9)3)

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