How do you expand #Ln( sqrt(a ^2 times b) /root4(b))#?

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Answer 1 · 2016-06-15T13:29:31

Use the rule #ln(a/n) = lna - lnn#.

#= lnsqrt(a^2b) - lnb^(1/4)#

#= ln(a^2b)^(1/2) - lnb^(1/4)#

Use the rule #loga^n = nlog#.

#= 1/2ln(a^2b) - 1/4lnb#

You can expand using the rule #ln(a xx b) = lna + lnb#.

#=1/2(lna^2 + lnb) - 1/4lnb#

#= 1/2lna^2 + 1/2lnb - 1/4lnb#

It is possible to simplify further but that would involve compressing. I don't know what you want...

Hopefully this helps!