$(2^{x+4})-(x^{x+2})=3$ find the value of x kindly help with step by step solution

Question

My teacher suggested $-2$ answer but I don't know how it would come kindly some one explain with step by step solution thank you

Answer 1

Substitute $-2$ for $x$ in $$(2^{x+4})-(x^{x+2})=3$$ and you get $$(2^{-2+4})-((-2)^{0})=3$$ That is $4-1 =3$

Thus $x=-2$ is a solution if we allow $(-2)^0 =1$

This is of course trial and error method which dose not carry much weight. An analytic solution does not seem possible.

Numerical methods gives a solution of $$x\approx 2.6735105$$ as a positive solution.