How do you expand #log_5(2sqrtm/n)#?

1 Answer
May 23, 2018

Answer:

It is #(\ln(2)+1/2*ln(m)-ln(n))/ln(5)#

Explanation:

Write #ln(2*sqrt(m)/n)/ln(5)=#
#(ln(2sqrt(m))-ln(n))/ln(5)=#
#(ln(2)+1/2ln(m)-ln(n))/ln(5)#
using that
#ln(ab)=ln(a)+ln(b)#
#log_ab=ln(b)/ln(a)#
#ln(a^r)=rln(a)#
all variables assumed to be positive.