Question #60774

1 Answer
May 9, 2016

Answer:

#x = (5+5e^4)/(e^4-1)~~5.187#

Explanation:

We will use the following properties of logarithms :

  • #ln(a)-ln(b) = log(a/b)# for #a, b > 0#
  • #e^ln(a) = a#

with these, we have

#ln(x+5)-ln(x-5) = 4#

(note that as the #ln# function only takes positive values, we must restrict #x# to be greater than #5#, or else we would have #x-5 < 0#)

#=> ln((x+5)/(x-5)) = 4#

#=> e^(ln((x+5)/(x-5))) = e^4#

#=> (x+5)/(x-5) = e^4#

#=> x + 5 = e^4x - 5e^4#

#=> e^4x - x = 5 + 5e^4#

#=> (e^4-1)x = 5+5e^4#

#:. x = (5+5e^4)/(e^4-1)~~5.187#