How do you simplify #ln 3 − 2(ln 4 + ln 8)#?

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Answer 1 · 2018-05-24T09:14:11

#ln3-2(ln4+ln8)=ln(3/1024)#

We use the identities #lna+lnb=ln(ab)#, #mlna=lna^m# and #lna-lnb=ln(a/b)#

Hence #ln3-2(ln4+ln8)#

= #ln3-2ln(4*8)#

= #ln3-2ln32#

= #ln3-ln(32^2)#

= #ln(3/32^2)#

= #ln(3/1024)#