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
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1Do you mean to solve the question $2^{x+4} - 2^{x+2} = 3$ instead? If so, you can factor out a $2^{x+2}$ on the left hand side. – Toby Mak Nov 29 '19 at 13:16
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1which level of mathematics are you learning at school @saria ? – Ahmad Bazzi Nov 29 '19 at 13:21
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I think the answer given by @Mohammad Riazi-Kermani is the proper way given your level. – Ahmad Bazzi Nov 29 '19 at 16:46
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I am learning business mathematics and it is elementary level question according to teacher – saria Nov 29 '19 at 16:53
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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.
Mohammad Riazi-Kermani
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I don`t think that $$x=-2 $$ is solution because we assume that $$ x>0$$ – vic165 Nov 29 '19 at 13:53
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You are correct. I do not know why the teacher suggested that as a solution. – Mohammad Riazi-Kermani Nov 29 '19 at 14:09