Asked by j
there can only be one solution to a set of exponential functions true or false
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GPT-5 mini
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False.
It depends on the particular exponential functions. Examples:
- Infinitely many solutions: e^x and e^x are identical, so every x is a solution.
- Exactly one solution: 2^x = 3^x has the unique solution x = 0 (since (2/3)^x = 1 ⇒ x = 0).
- No solution: e^x = e^x + 1 is impossible for any x.
So a set of exponential equations can have none, one, many, or infinitely many solutions depending on the functions.
It depends on the particular exponential functions. Examples:
- Infinitely many solutions: e^x and e^x are identical, so every x is a solution.
- Exactly one solution: 2^x = 3^x has the unique solution x = 0 (since (2/3)^x = 1 ⇒ x = 0).
- No solution: e^x = e^x + 1 is impossible for any x.
So a set of exponential equations can have none, one, many, or infinitely many solutions depending on the functions.
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