Résoudre une inéquation contenant des exponentielles - Première

Takeaways

• 😀 Exponential functions can be tricky when solving inequalities, but there are techniques to simplify them.
• 😀 The inequality given in the video is: exp(4x - 1) ≥ 1.
• 😀 If you're unfamiliar with solving exponential equations, it’s recommended to watch a prior video on the subject.
• 😀 The key to solving exponential inequalities is eliminating the exponential function to use known algebraic techniques.
• 😀 One property of exponential functions is that if exp(a) ≤ exp(b), then a ≤ b, as the exponential function is strictly increasing.
• 😀 In this case, the problem is that we don’t have exp(a) ≥ exp(b), but this can be resolved by rewriting 1 as exp(0).
• 😀 Rewriting the inequality exp(4x - 1) ≥ exp(0) allows the exponential terms to be eliminated using the aforementioned property.
• 😀 After simplifying, the inequality becomes a linear inequality: 4x - 1 ≥ 0.
• 😀 Solving the linear inequality results in x ≥ 1/4.
• 😀 The solution to the inequality is all values of x greater than or equal to 1/4, extending infinitely.
• 😀 This method of transforming exponential inequalities into simpler linear ones is a standard technique in algebra.