Question 26641
 3coshx + 5sinhx = 8
FOR SIMPLICITY LET US DENOTE ....E^X=A...SO ...E^(-X)=1/A...HENCE 
COSH X = (A+1/A)/2...AND .....SINH X=(A-1/A)/2...SO WE HAVE 
3(A+1/A)/2+5(A-1/A)/2=8...MULTIPLYING BY 2
3A+3/A+5A-5/A=16
8A-2/A=16.....DIVIDING BY 2 WE GET 
4A-1/A-8=0....OR MULTIPLYING BY A...
4A^2-8A-1=0
USING QUADRATIC FORMULA..{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
WE GET  ..{{{a = (8 +- sqrt( 64+16 ))/(2*4) }}}
..{{{a = (8 +- sqrt( 80 ))/(8) }}}
..{{{a = (8 +-4* sqrt( 5 ))/(8) }}}
..{{{a = (1 +-0.5* sqrt( 5 )) }}}=E^X...WHERE FROM YOU CAN GET X USING LOGS
X=LN{1+0.5(0.5)^(0.5)}