the graph of y=ax^n includes the point (-3,-2187) when a=-1. what is the value of n

Answer 1

Since a<0 let's set a=-b, y=-u,

so b>0 and we have

-u=(-b)xⁿ, or u=bxⁿ.

When y<0, u>0. Since b>0, so there must have xⁿ > 0 for any x, which means n must be an even integer, and we have xⁿ = (-x)ⁿ.

When x<0, we do log on both sides of the equation:

log u = log b + n log (-x),

so

n = (log u - log b) / log (-x) = (log2187-log1)/log3=7

The result of n=7 is against the requirement that n be an even integer, therefore there is no solution for this problem.