document.write( "Question 311598: Use the change of base formula to evaluate \"log%282%2C17%29\" \n" ); document.write( "
Algebra.Com's Answer #222861 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Use the change of base formula to evaluate \"log%282%2C17%29\"
\n" ); document.write( "
\r\n" );
document.write( "Change of base formula:\r\n" );
document.write( "\r\n" );
document.write( "\"log%28OLD_BASE%2C%28X%29%29\"\"%22=%22\"\"log%28NEW_BASE%2C%28X%29%29%2Flog%28NEW_BASE%2C%28OLD_BASE%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "The \"OLD_BASE\" is 2 and the \"NEW_BASE\" is either 10 or e, take your pick:\r\n" );
document.write( "\r\n" );
document.write( "If we pick 10 for the \"NEW_BASE\", then\r\n" );
document.write( "\r\n" );
document.write( "\"log%28OLD_BASE%2C%28X%29%29\"\"%22=%22\"\"log%28NEW_BASE%2C%28X%29%29%2Flog%28NEW_BASE%2C%28OLD_BASE%29%29\"\r\n" );
document.write( "becomes\r\n" );
document.write( "\"log%282%2C%2817%29%29\"\"%22=%22\"\"log%2810%2C%2817%29%29%2Flog%2810%2C%282%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "When the base is 10 we don't write the 10 but leave it understood:\r\n" );
document.write( "\"log%282%2C%2817%29%29\"\"%22=%22\"\"log%28%2817%29%29%2Flog%28%282%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Then we cet a calculator and find those logarithms with the LOG key:\r\n" );
document.write( "\"log%282%2C%2817%29%29\"\"%22=%22\"\"1.230448921%2F0.3010299957=4.08746284\"\r\n" );
document.write( "--------------------------------------------\r\n" );
document.write( "If we pick e for the \"NEW_BASE\", then\r\n" );
document.write( "\r\n" );
document.write( "\"log%28OLD_BASE%2C%28X%29%29\"\"%22=%22\"\"log%28NEW_BASE%2C%28X%29%29%2Flog%28NEW_BASE%2C%28OLD_BASE%29%29\"\r\n" );
document.write( "becomes\r\n" );
document.write( "\"log%282%2C%2817%29%29\"\"%22=%22\"\"log%28e%2C%2817%29%29%2Flog%28e%2C%282%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "When the base is e we don't write \"log%28e%2C%22%22%29\" but write \"ln%28%22%22%29\" instead:\r\n" );
document.write( "\"log%282%2C%2817%29%29\"\"%22=%22\"\"ln%2817%29%2Fln%282%29\"\r\n" );
document.write( "\r\n" );
document.write( "Then we cet a calculator and find those natural logarithms with the LN key:\r\n" );
document.write( "\"log%282%2C%2817%29%29\"\"%22=%22\"\"2.833213344%2F0.6931471806=4.087462841\"\r\n" );
document.write( "\r\n" );
document.write( "Notice that regardless of whether we picked 10 or e for the \"NEW_BASE\",\r\n" );
document.write( "we ended up with the same answer.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );