document.write( "Question 1039561: Use the properties of exponents to prove the Power Property of Logarithms. \n" ); document.write( "

Algebra.Com's Answer #654384 by Edwin McCravy(20065) $\"\"$ $\"About$

You can put this solution on YOUR website!

   \r\n" );
document.write( "The power property of logarithms, which we \r\n" );
document.write( "are to prove, is\r\n" );
document.write( "\r\n" );
document.write( "(1)   \r\n" );
document.write( "\r\n" );
document.write( "But first we prove this: \r\n" );
document.write( "\r\n" );
document.write( "(2)     \r\n" );
document.write( "\r\n" );
document.write( "-----------------\r\n" );
document.write( "\r\n" );
document.write( "Let \r\n" );
document.write( "\r\n" );
document.write( "Then by definition of logarithm\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substitute for x\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So we have proved (2).\r\n" );
document.write( "\r\n" );
document.write( "-----------------\r\n" );
document.write( "\r\n" );
document.write( "Let \r\n" );
document.write( "\r\n" );
document.write( "Then by the definition of logarithm:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Using (2) to replace A\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Use the rule of multiplying \r\n" );
document.write( "exponents on the right:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Equate the powers of B\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So we have proved (1)\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );