- #1

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i heard there is some way of solving for x, but i can't for the life of me remember how. please help!

ln(x) + x = 10

thanks!!!

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- Thread starter j3n
- Start date

- #1

- 3

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i heard there is some way of solving for x, but i can't for the life of me remember how. please help!

ln(x) + x = 10

thanks!!!

- #2

- 1,039

- 3

lnx>=1

x>=e...(1)

lnx>=1

lnx+x>=1+x

1+x<=10

x<=9

solution set for x: [e,9]

- #3

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Graph intersection: y=ln x and y=10-x.

- #4

Gib Z

Homework Helper

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>.< I don't think thats it mate.

Theres no way to solve for x, you can only approximate it.

Theres no way to solve for x, you can only approximate it.

- #5

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we will need, the function:

f (x) = ln(x) + x -10 = 0

and its first derivative:

f'(x) = 1/x + 1

an initial guess:

x0 = 1

and we can begin:

x1 = x0 - f(x0)/f'(x0) = 5.5

x2 = x1 - f(x1)/f'(x1) = 7.865213153

x3 = 7.929390693

x4 = 7.929420095

x5 = x4 as far as my calculator is concerned

try it out

- #6

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Just curious how you would use Newton's Method, Gib Z, since you do not use a calculator.

Cheers,

Cheers,

Last edited:

- #7

HallsofIvy

Science Advisor

Homework Helper

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i heard there is some way of solving for x, but i can't for the life of me remember how. please help!

ln(x) + x = 10

thanks!!!

I wonder if you are not thinking of the "Lambert W function". W(x) is defined as the inverse of the function f(x)= xe

If ln(x)+ x= 10, then, taking the exponential of each side, e

x= W(e

Of course, the only way to evaluate that is to do some kind of numerical approximation as others have said,

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