How do you expand log_5(2sqrtm/n)log5(2√mn)?

1 Answer
Sonnhard
May 23, 2018

It is (\ln(2)+1/2*ln(m)-ln(n))/ln(5)ln(2)+12⋅ln(m)−ln(n)ln(5)

Explanation:

Write ln(2*sqrt(m)/n)/ln(5)=ln(2⋅√mn)ln(5)=
(ln(2sqrt(m))-ln(n))/ln(5)=ln(2√m)−ln(n)ln(5)=
(ln(2)+1/2ln(m)-ln(n))/ln(5)ln(2)+12ln(m)−ln(n)ln(5)
using that
ln(ab)=ln(a)+ln(b)ln(ab)=ln(a)+ln(b)
log_ab=ln(b)/ln(a)logab=ln(b)ln(a)
ln(a^r)=rln(a)ln(ar)=rln(a)
all variables assumed to be positive.

Related questions
See all questions in Common Logs
Impact of this question
1568 views around the world
You can reuse this answer
Creative Commons License