Solve the equation #4e^x-15e^(-x)-4=0#?

Question

262 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-17T14:08:29

#x=0.9163#

As #4e^x-15e^(-x)-4=0#, multiplying each term by #e^x# we have

#4(e^x)^2-15-4e^x=0#.

Now let #e^x=u#. then the above equation becomes

#4u^2-4u-15=0#

i.e. #(2u-5)(2u+3)=0# i.e. #u=5/2# or #-3/2#

But as #u=e^x#, range of #u# is #(0,oo)# and we cannot have #u=-3/2#

Hence #u=5/2# or #e^x=5/2=2.5#

and #x=ln2.5=0.9163#