- #1

- 33

- 1

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

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- 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

- 3,798

- 94

- #3

- 33

- 1

I will also have a look at Lambert W Function.

Thanks

- #4

Mentallic

Homework Helper

- 3,798

- 94

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

- 711

- 170

- #6

- 33

- 1

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

- #7

HallsofIvy

Science Advisor

Homework Helper

- 41,847

- 966

- #8

- 15

- 1

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

Share: