document.write( "Question 240209: solve the exponential equation.\r
\n" );
document.write( "\n" );
document.write( "e^2x + e^x -6=0 \n" );
document.write( "
Algebra.Com's Answer #176067 by nerdybill(7384)![]() ![]() You can put this solution on YOUR website! e^2x + e^x -6=0 \n" ); document.write( ". \n" ); document.write( "This is simply a \"quadratic equation\": \n" ); document.write( ". \n" ); document.write( "Let y = e^x \n" ); document.write( "then \n" ); document.write( "y^2 = (e^x)^2 = (e^x)(e^x) = e^2x \n" ); document.write( ". \n" ); document.write( "So now we can rewrite: \n" ); document.write( "e^2x + e^x -6=0 \n" ); document.write( "y^2 + y -6=0 \n" ); document.write( "(y+3)(y-2) = 0 \n" ); document.write( "y = {-3, 2} \n" ); document.write( ". \n" ); document.write( "Since we said: \n" ); document.write( "y = e^x \n" ); document.write( "ln y = x \n" ); document.write( ". \n" ); document.write( "So, \n" ); document.write( "x = ln 2 (this is your solution) \n" ); document.write( " \n" ); document.write( " |