How do you expand # ln(sqrt13.5)#?

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Answer 1 · 2017-04-07T15:21:43

Please see the explanation.

Write the square root as the #1/2# power:

#ln((13.5)^(1/2))#

Write #13.5# as #27/2#:

#ln((27/2)^(1/2))#

Use the property #ln(a^c) = (c)ln(a)#:

#1/2(ln(27/2))#

Use the property #ln(a/c) = ln(a) - ln(c)#

#1/2(ln(27) -ln(2))#

You can distribute the #1/2#, if you like but I think this is fine.