document.write( "Question 1153082: https://imgur.com/a/nHNVzJD Find log(base z)w \n" ); document.write( "
Algebra.Com's Answer #775279 by ikleyn(52879)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "You are given\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"log%28x%2C%28w%29%29\" = \"24\",  \"log%28y%2C%28w%29%29\" = \"40\",  \"log%28xyz%2C%28w%29%29\" = \"12\".    (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "They want you find \"log%28z%2C%28w%29%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Solution\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From (1), you have, using the change of base formula\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"log%28w%2C+%28x%29%29\" = \"1%2F24\";  \"log%28w%2C+%28y%29%29\" = \"1%2F40\"  and  \"log%28w%2C+%28xyz%29%29\" = \"1%2F12\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Transform the last equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"log%28w%2C++%28xyz%29%29\" = \"1%2F12\" = \"log%28w%2C+%28x%29%29\" + \"log%28w%2C+%28y%29%29\" + \"log%28w%2C+%28z%29%29\" = \"1%2F24\" + \"1%2F40\" + \"log%28w%2C+%28z%29%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It implies\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"log%28w%2C+%28z%29%29\" = \"1%2F12\" - \"1%2F24\" - \"1%2F40\" = \"10%2F120+-+5%2F120+-+3%2F120\" = \"2%2F120\" = \"1%2F60\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence,  \"log%28z%2C+%28w%29%29\" = \"1%2Flog%28w%2C+%28z%29%29\" = \"1%2F%28%281%2F60%29%29\" = 60.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  \"log%28z%2C+%28w%29%29\" = 60.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "T h a t ' s     a l l.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            +---------------------------------------------------------+
\n" ); document.write( "            |   It is how this problem  SHOULD  BE  SOLVED.   |
\n" ); document.write( "            +---------------------------------------------------------+\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For your safety,  IGNORE  everything that  @MathLover1 wrote in her post.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "This woman demonstrates extreme activity,  but solves many problems  INCORRECTLY,  or in a way,
\n" ); document.write( "which is not adequate and/or is not effective.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Unfortunately.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So,  be careful,  considering her contribution  (!)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );