document.write( "Question 46884: Solve the equation 3log5 x - log5 4 = log5 16 \n" ); document.write( "
Algebra.Com's Answer #854287 by MathTherapy(10837)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Solve the equation 3log5 x - log5 4 = log5 16\r\n" );
document.write( "*********************************************\r\n" );
document.write( "Everything that the other person, consc198(59), did, was WRONG. He/she contends that:\r\n" );
document.write( "\"3log5 x - log5 x 4 = log5 x 16\r\n" );
document.write( "2.096910013 x -0.698970004 x 4 = 0.698970004 x 16\r\n" );
document.write( "2.096910013 x -2.795880016 = 11.18352006\r\n" );
document.write( "-5.862708801 = 11.18352006\r\n" );
document.write( "11.18352006 + 5.862708801\r\n" );
document.write( "Answer = 17.04622886\"\r\n" );
document.write( "*******\r\n" );
document.write( "This is CERTAINLY NOT the way to solve a LOGARITHMIC equation. Furthermore, the answer is\r\n" );
document.write( "CERTAINLY NOT 17.04622886. Instead, it's done PRECISELY as follows:\r\n" );
document.write( "\"3%2Alog+%285%2C+%28x%29%29+-+log+%285%2C+%284%29%29+=+log+%285%2C+%2816%29%29\"\r\n" );
document.write( "\"log+%285%2C+%28x%5E3%29%29+-+log+%285%2C+%284%29%29+=+log+%285%2C+%2816%29%29\" ---- Applying \"a%2Alog+%28b%2C+%28c%29%29\" = \"log+%28b%2C+%28c%5Ea%29%29\" \r\n" );
document.write( "              \"log+%285%2C+%28x%5E3%2F4%29%29+=+log+%285%2C+%2816%29%29\" ---- Applying \"log+%28b%2C+%28c%29%29+-+log+%28b%2C+%28d%29%29+=+log+%28b%2C+%28c%2Fd%29%29\"\r\n" );
document.write( "                           \"x%5E3%2F4+=+16\" ---- If \"log+%28b%2C+%28c%29%29+=+log+%28b%2C+%28d%29%29\", then c = d\r\n" );
document.write( "                           \"x%5E3+=+64\" ------ Cross-multiplying\r\n" );
document.write( "                      \"root%283%2C+x%5E3%29+=+root+%283%2C+64%29\" --- Taking the CUBE ROOT of each side\r\n" );
document.write( "                             x = 4
\n" ); document.write( "
\n" );