- #1

- 33

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I was trying to solve the Inequality x+3

^{x}<4 and i found the solution to be x<1, using trial and error.

Is there another Logical way or analytic one.

Thanks

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- Thread starter Karim Habashy
- Start date

- #1

- 33

- 1

I was trying to solve the Inequality x+3

Is there another Logical way or analytic one.

Thanks

- #2

Mentallic

Homework Helper

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- #3

- 33

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I will also have a look at Lambert W Function.

Thanks

- #4

Mentallic

Homework Helper

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Just to be clear, proving that the equation cannot hold for x>1 is NOT a proof by contradiction. You can't automatically assume that if x>1 does not satisfy the inequality, then x<1 must satisfy it. It doesn't work that way.

I'd suggest calculus for showing that there are no values x>1 that satisfy the equation.

- #5

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- #6

- 33

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How do i use calculus ?, the function is monotonically increasing.

- #7

HallsofIvy

Science Advisor

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- #8

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Trial and error is the way to go, unless you want to put the log product function into play.

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