How do you condense 4 ln 2 - ln 3 - 1?

1 Answer
Feb 25, 2017

4ln2-ln3-1=ln(16/(3e))

Explanation:

4ln2-ln3-1

We know that: alnb=lnb^a, therefore,

=ln2^4-ln3-1
=ln16-ln3-1

We know that: lna-lnb=ln(a*1/b), therefore,

=ln(16*1/3)-1
=ln(16/3)-1

We know that: lne=1, therefore,

=ln(16/3)-lne
=ln(16/3*1/e)
=ln(16/(3e))

Hence, 4ln2-ln3-1=ln(16/(3e))