Posted by Helga on Thursday, March 1, 2012 at 2:53am. cross
multiply to get: Since there is no more division and the right-
hand side is less than 1, we can start searching for n where
n<1, say 1/2. Try n=1/2 and see if the equation is satisfied.
Hint: one of the laws of exponents tells us that Is there a more
elegant solution than trial and error? You have an excellent
question! In other words, your question was more like: Find all
solutions for n such that I do not see an explicit solution to
the equation. Perhaps someone else can find one. An explicit
solution is expressed as n=expression where expression does not
contain n. Lack of an explicit solution, I proceed as follows:
1. first bound the solution. We can conclude that for n outside
of [-1,1], we cannot have the right hand side equal to -1. 2.
Find approximate solutions by graphing or otherwise. By
graphing, there are two solutions, at 0.5 and 0.8,
approximately. 3. proceed to refine the solutions by iterations
(a glamorous name for trial and error).