SOLUTION: Show that for all k and all v>0, ln(v^k) = k(ln v) and log(v^k) = k(log v)

Question 443211: Show that for all k and all v>0, ln(v^k) = k(ln v) and log(v^k) = k(log v)
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
Let
Then
Raise both sides to the n power.
=
ln both sides:

Remember that
Then

Q.E.D. :)
--------------------
Let
Then v =
Raise both sides to the n power

log both sides

Substitute for m back

--------------------
Hope this helped!

RELATED QUESTIONS
Solve for v.... (answered by jim_thompson5910)

1. K > ~K 2. (~S v U)> K /... (answered by lynnlo,jim_thompson5910)

Q=m-v/k solve for... (answered by Alan3354)

v=(b-u)/k solve for... (answered by Gogonati)

K=1/2mv^2 solve for... (answered by greenestamps)