document.write( "Question 1080329: solve for x if (2e^x-e^(-x))/5=t \n" ); document.write( "

Algebra.Com's Answer #694505 by Fombitz(32388) $\"\"$ $\"About$

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Let $\"u=e%5Ex\"$ ,
\n" ); document.write( " $\"2u-1%2Fu=5t\"$
\n" ); document.write( " $\"2u%5E2-1=5ut\"$
\n" ); document.write( " $\"2u%5E2-5ut-1=0\"$
\n" ); document.write( "Using the quadratic equation,
\n" ); document.write( " $\"u=%28-%28-5t%29%2B-sqrt%28%28-5t%29%5E2-4%282%29%28-1%29%29%29%2F%282%282%29%29\"$
\n" ); document.write( " $\"u=%285t%2B-sqrt%2825t%5E2%2B8%29%29%2F4\"$
\n" ); document.write( " $\"e%5Ex=%285t+%2B-+sqrt%2825t%5E2%2B8%29%29%2F4\"$
\n" ); document.write( "The solution with the negative sign would give a negative right hand side which would have no solution so we remove that portion,
\n" ); document.write( " $\"e%5Ex=%285t+%2B+sqrt%2825t%5E2%2B8%29%29%2F4\"$
\n" ); document.write( " $\"x=ln%28%285t+%2B+sqrt%2825t%5E2%2B8%29%29%2F4%29\"$ \n" ); document.write( "

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