document.write( "Question 1138795: Please help me solve for x in
\n" ); document.write( "4logx to base 16 = log(x + 12) to base 4 \n" ); document.write( "
Algebra.Com's Answer #756602 by ikleyn(52803)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "The original equation is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"4%2Alog%2816%2C%28x%29%29\" = \"log%284%2C%28x%2B12%29%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Note that the domain, where both sides are defined, is the set of positive real x:  { x | x > 0 }.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Due to properties of logarithms, it is the same as\r\n" );
document.write( "\r\n" );
document.write( "     \"4%2A%281%2F2%29%2Alog%284%2C%28x%29%29\" = \"log%284%2C%28x%2B12%29%29\",   or, equivalently,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     \"2%2Alog%284%2C%28x%29%29\" = \"log%284%2C%28x%2B12%29%29\",   which, in turn, is equivalent to\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     \"log%284%2C%28x%5E2%29%29\" = \"log%284%2C%28x%2B12%29%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It implies\r\n" );
document.write( "\r\n" );
document.write( "      x^2 = x + 12\r\n" );
document.write( "\r\n" );
document.write( "      x^2 - x - 12 = 0,\r\n" );
document.write( "\r\n" );
document.write( "      (x-4)*(x+3) = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Of the two roots, x= 4 and x= -3, only positive x= 4 is in the domain and is, therefore, the solution.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  x= 4.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.   //   I mean,  solved in a way as it should be done.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "--------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "On the way,  I used standard and elementary properties of logarithms that every student must learn and must know
\n" ); document.write( "before starting solving such problems.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "On logarithms and their properties,  see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - WHAT IS the logarithm \r
\n" ); document.write( "\n" ); document.write( "    - Properties of the logarithm \r
\n" ); document.write( "\n" ); document.write( "    - Change of Base Formula for logarithms \r
\n" ); document.write( "\n" ); document.write( "    - Solving logarithmic equations \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Logarithms\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );