How do I convince students in high school for which

Helen Lewis

Helen Lewis

Answered question

2022-01-04

How do I convince students in high school for which this equation: 2x=4x have only one solution in integers that is x=4?

Answer & Explanation

encolatgehu

encolatgehu

Beginner2022-01-05Added 27 answers

Hint:
plot the graph of y=2x and y=4x and shows that the only other solution is between 0 and 1.
Jeffery Autrey

Jeffery Autrey

Beginner2022-01-06Added 35 answers

If your intention is to 'convince' and not to prove, I'd draw a graph with the functions y=2x  and  y=4x.The growth rate of each function should make clear that they intersect only at two points, being the first between 0 and 1 (and hence, not being an integer).
Vasquez

Vasquez

Expert2022-01-11Added 669 answers

For positive n, we have two growing sequences
1,2,4,8,16,32,64,128,256⋯
0,4,8,12,16,20,24,28,32⋯
This shows them that the ''curves'' cross each other at 16, and it seems that the first grows faster.
Indeed, taking the ratios of successive terms
2n+12n=2>4(n+1)4n=1+1n

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