document.write( "Question 443211: Show that for all k and all v>0, ln(v^k) = k(ln v) and log(v^k) = k(log v) \n" ); document.write( "

Algebra.Com's Answer #305742 by swincher4391(1107) $\"\"$ $\"About$

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