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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Let m+=+ln%28v%29
Then v+=+e%5Em
Raise both sides to the n power.
v%5En = %28e%5Em%29%5En
ln both sides:
ln%28v%5En%29+=+mn
Remember that m+=+ln%28v%29
Then ln%28v%5En%29+=+ln%28v%29+%2A+n
ln%28v%5En%29+=+n%2Aln%28v%29
Q.E.D. :)
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Let m+=+log%28v%29
Then v = 10%5Em
Raise both sides to the n power
v%5En+=+%2810%5Em%29%5En
log both sides
log%28v%5En%29+=+mn
Substitute for m back
log%28v%5En%29+=+log%28v%29%2An
log%28v%5En%29+=+n%2Alog%28v%29
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Hope this helped!