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

Lorena Becker

Lorena Becker

Answered question

2022-11-26

How do I convince students in high school for which this equation: 2 x = 4 x have only one solution in integers that is x = 4?
I would like to convince my student in high school level using a simple mathematical way to solve this equation:
2 x = 4 x
have only one solution that is x = 4?
Note : I do not want to use substitution to convince them and by numerical methods can't give us exactly x = 4
EDIT: I edited the question as it is very related to the precedent
Thank you for any help.

Answer & Explanation

Lekmarjuqw4

Lekmarjuqw4

Beginner2022-11-27Added 9 answers

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

zweifelndcuv

Beginner2022-11-28Added 1 answers

If your intention is to 'convince' and not to prove, I'd draw a graph with the functions y = 2 x and y = 4 x. 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).

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