document.write( "Question 258691: How would I solve:\r
\n" ); document.write( "\n" ); document.write( "ln ( x + 3 ) - ln ( x + 2 ) = 5\r
\n" ); document.write( "\n" ); document.write( "I know that you have to divide so I got: ln ( x+3/x+2) = 5 but I couldn't get any farther than that.
\n" ); document.write( "

Algebra.Com's Answer #190430 by Edwin McCravy(20062)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "You just need to learn how to change a logarithm equation \r\n" );
document.write( "to an exponential equation:\r\n" );
document.write( "\r\n" );
document.write( "If it's a log base b equation like this:\r\n" );
document.write( "\r\n" );
document.write( "\"log%28b%2C%28%22EXPRESSION%231%22%29%29+=+%22EXPRESSION%232%22\"\r\n" );
document.write( "\r\n" );
document.write( "you change it to this exponential form:\r\n" );
document.write( "\r\n" );
document.write( "\"%22EXPRESSION%231%22=b%5E%28%22EXPRESSION%232%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "If it's a natural log equation, (like yours), like this:\r\n" );
document.write( "\r\n" );
document.write( "\"ln%28%22EXPRESSION%231%22%29+=+%22EXPRESSION%232%22\"\r\n" );
document.write( "\r\n" );
document.write( "you change it to this exponential form:\r\n" );
document.write( "\r\n" );
document.write( "\"%22EXPRESSION%231%22=e%5E%28%22EXPRESSION%232%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "You can think of the instructions\r\n" );
document.write( "this way:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Drop the log on one side and put the \r\n" );
document.write( "other side as an exponent of the base.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So when you got here:\r\n" );
document.write( "\r\n" );
document.write( "\"ln+%28+%28x%2B3%29%2F%28x%2B2%29%29+=+5\"\r\n" );
document.write( "\r\n" );
document.write( "You drop the \"ln\" on the left and put the right side\r\n" );
document.write( "as an exponent of \"e\" like this:\r\n" );
document.write( "\r\n" );
document.write( "\"%28x%2B3%29%2F%28x%2B2%29+=+e%5E5\"\r\n" );
document.write( "\r\n" );
document.write( "Then you clear of fractions by multiplying\r\n" );
document.write( "both side by \"%28x%2B2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"x%2B3=e%5E5%28x%2B2%29\"\r\n" );
document.write( "\r\n" );
document.write( "Distribute on the right:\r\n" );
document.write( "\r\n" );
document.write( "\"x%2B3=e%5E5%2Ax%2B2e%5E5%29\"\r\n" );
document.write( "\r\n" );
document.write( "Get the x-terms on the left\r\n" );
document.write( "and the other terms on the right:\r\n" );
document.write( "\r\n" );
document.write( "\"x-e%5E5%2Ax=2e%5E5-3\"\r\n" );
document.write( "\r\n" );
document.write( "Factor out x on the left:\r\n" );
document.write( "\r\n" );
document.write( "\"x%281-e%5E5%29=2e%5E5-3\"\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by \"1-e%5E5\"\r\n" );
document.write( "\r\n" );
document.write( "\"x=%282e%5E5-3%29%2F%281-e%5E5%29\"\r\n" );
document.write( "\r\n" );
document.write( "You can either leave it like that or\r\n" );
document.write( "get your calculator and punch it out\r\n" );
document.write( "and get the decimal approximation:\r\n" );
document.write( "\r\n" );
document.write( "\"x=-1.993216345\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );