Question

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

Answer 1

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.