Slove the equation cosh(lnx) =2sinh(ln)-1?
1 Answer
Mar 13, 2018
# x=-1,3 #
Explanation:
We have:
# cosh(lnx) = 2sinh(lnx)-1 #
Let us use the exponential definitions of
# coshx=(e^x+e^(-x))/2 \ \ # and# sinhx=(e^x-e^(-x))/2 #
Giving us:
# (e^(lnx)+e^(-(lnx)))/2 = 2 (e^(lnx)-e^(-(lnx)))/2 - 1#
# :. e^(lnx)+e^(ln(1/x)) = 2(e^(lnx)-e^(ln(1/x))) - 2#
# :. x + 1/x = 2(x - 1/x) - 2#
# :. x + 1/x = 2x - 2/x - 2#
# :. x - 3/x - 2 = 0#
# :. (x^2-2x-3)/x = 0#
# :. ((x-3)(x+1))/x = 0#
# :. x=-1,3 #
