Question #fb22f

1 Answer
Dec 10, 2017

#x = 1 + sqrt2 #

Explanation:

We must use our definitions of #sinhx#:

#sinhx = 1/2 ( e^x - e^-x ) #

So hence:

#=> sinh(lnx) = 1/2 ( e^lnx - e^(-lnx) ) #

Using our log laws:

#e^lnx = x and -lnx = ln(1/x) #

#=> sinh(lnx) = 1/2 ( x -1/x )#

#sinh(lnx) = 1#:

#=> 1/2 (x- 1/x ) =1 #

#=> x-1/x = 2 #

#=> x^2 - 2x -1 = 0#

Using the quadraric formula:

# x = 1 pm sqrt2 #

But it cant be #1-sqrt 2 # as: #ln(1-sqrt2 ) notin RR#

So hence #x = 1 + sqrt2 #