document.write( "Question 281235: write a rule for log (a)^m. Then use the idea of powers of ten to argue that your rule works for any m and all values of a 0.\r
\n" ); document.write( "\n" ); document.write( "I suppose that log (am)^m = m log a, but how do i use the idea of powers of ten to prove? Please help!\r
\n" ); document.write( "\n" ); document.write( "Note: this problem is meant to help me figure out the power property of log:
\n" ); document.write( "log(lower case b) (a^n) = n x log(lower case b)(a) \n" ); document.write( "
Algebra.Com's Answer #204338 by dabanfield(803)\"\" \"About 
You can put this solution on YOUR website!
write a rule for log (a)^m. Then use the idea of powers of ten to argue that your rule works for any m and all values of a 0.
\n" ); document.write( "I suppose that log (am)^m = m log a, but how do i use the idea of powers of ten to prove? Please help!
\n" ); document.write( "Note: this problem is meant to help me figure out the power property of log:
\n" ); document.write( "log(lower case b) (a^n) = n x log(lower case b)(a)\r
\n" ); document.write( "\n" ); document.write( "Show why it makes sense that the log (a)^n = n*log a.\r
\n" ); document.write( "\n" ); document.write( "Remember 10^n = 10*10*10...*10 (n 10's).\r
\n" ); document.write( "\n" ); document.write( "So we have:\r
\n" ); document.write( "\n" ); document.write( "1.) log 10^n = log (10*10*10...*10) (n 10's)\r
\n" ); document.write( "\n" ); document.write( "Using the log rule that says log (a*b) = log a + log b then 1.) above becomes:\r
\n" ); document.write( "\n" ); document.write( "log 10^n = log 10 + log 10 + log 10 +...+ log 10 (n log 10's) so\r
\n" ); document.write( "\n" ); document.write( "log 10^n = n*log 10\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );