document.write( "Question 719905: e^x-e^-x=10 \n" ); document.write( "
Algebra.Com's Answer #441675 by jsmallt9(3758)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "Rewriting \n" ); document.write( " \n" ); document.write( "First, we'll eliminate the fraction by multiplying both sides by \n" ); document.write( " \n" ); document.write( "which simplifies to: \n" ); document.write( " \n" ); document.write( "Next we'll get a zero on the right side by subtracting \n" ); document.write( " \n" ); document.write( "This does not factor, unfortunately. \n" ); document.write( "This next part is probably the hardest part. The exponent of \n" ); document.write( "Let \n" ); document.write( " \n" ); document.write( "This is clearly an quadratic equation. As noted earlier, this will not factor. But we can use the quadratic formula: \n" ); document.write( " \n" ); document.write( "Simplifying... \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "which is short for: \n" ); document.write( " \n" ); document.write( "Of course we are not interested in solutions for q. We are interested in solutions for x. So now we substitute back for the q: \n" ); document.write( " \n" ); document.write( "We have a little more work to do to solve for x. Since \n" ); document.write( "So our only solution(s) will come from the first equation. Finding the ln of each side: \n" ); document.write( " \n" ); document.write( "On the left side we use a property of logs, \n" ); document.write( " \n" ); document.write( "Since ln(e) = 1 the left side becomes: \n" ); document.write( " \n" ); document.write( "This is an exact expression for the solution to your equation. If you want/need a decimal approximation, get out your calculator. \n" ); document.write( "P.S. After you have done a few of these quadratic form equations, you will not need a temporary variable. You will start to see how to go directly from: \n" ); document.write( " \n" ); document.write( "to \n" ); document.write( " \n" ); document.write( "etc. \n" ); document.write( " |