Question 714848
{{{ ( e^x + 9*e^(-1) - 1 ) / 2 = 3 }}}
{{{  e^x + 9*e^(-1) - 1  = 6 }}} 
{{{  e^x + 9*e^(-1) = 7 }}} 
{{{ e^x = 7 - 9*e^(-1) }}}
Multiply both sides by {{{ e }}}
{{{ e^( x + 1 ) = 7e - 9 }}}
Take the natural log of both sides
{{{  x + 1 = ln( 7e - 9 ) }}}
(a)
{{{ x = ln( 7e - 9 ) - 1 }}}
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(b)
{{{ e = 2.71828 }}}
{{{ x = ln( 7*2.71828 - 9 ) - 1 }}}
{{{ x = ln( 19.02797 - 9 ) - 1 }}}
{{{ x = ln( 10.02797 ) - 1 }}}
{{{ x = 2.30538 - 1 }}}
{{{ x = 1.30538 }}}
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check answer:
{{{ ( e^x + 9*e^(-1) - 1 ) / 2 = 3 }}}
{{{ ( e^1.30538 + 9/2.71828 - 1 ) / 2 = 3 }}}
{{{ ( 3.689091 + 3.310917 - 1 ) / 2 = 3 }}}
{{{ ( 7.0000082 - 1 ) / 2 = 3 }}}
{{{ 6.0000082 = 6 }}}
close enough