How do you expand ln(√(3−2)(53)(2−2))?

1 Answer
Lucio Falabella
Jan 8, 2016

ln(√3−3⋅53⋅2−2)=12(3ln(5)−2ln(2)−3ln(3))

Explanation:

Given that ln(x)=logex
and are satisfied:
x>0,e>0,e≠1

We can apply the logarithmic properties:

ln(a⋅b)=ln(a)+ln(b)
ln(ab)=ln(a)−ln(b)
ln(ab)=bln(a)

and remembering that:

amn=n√am
a−m=1am

then:

ln(√3−3⋅53⋅2−2)=ln((3−3⋅53⋅2−2)12)=
=12ln(3−3⋅53⋅2−2)=12(ln(3−3)+ln(53)+ln(2−2))=
=12(−3ln(3)+3ln(5)−2ln(2))

Alternitevely:

ln((3−3⋅53⋅2−2)12)=12ln(3−3⋅53⋅2−2)=
=12ln(5333⋅22)=
=12(ln(53)−ln(33)−ln(22))=
=12(3⋅ln(5)−3ln(3)−2ln(2))

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