Could someone help please.

I don't know how to solve this

I know the answer is approx 1.8536 (Wolfram alpha)

and I know what the graph looks like (Desmos)

I have played with it but I have not had any success.

Thank you.

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- Jan 16th 2014, 03:39 PM #1

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## e^x+lnx=7

Could someone help please.

I don't know how to solve this

I know the answer is approx 1.8536 (Wolfram alpha)

and I know what the graph looks like (Desmos)

I have played with it but I have not had any success.

Thank you.

- Jan 16th 2014, 04:03 PM #2
## Re: e^x+lnx=7

There is no simple solution.

But you need to understand Newton Method.

- Jan 16th 2014, 04:39 PM #3

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- Jan 17th 2014, 02:07 AM #4

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## Re: e^x+lnx=7

Newton's method, also known as the Newton-Raphson method, is probably the first method that would spring to mind. For this example though a simple fixed point iteration will suffice.

Rewrite the equation as

from which form the iterative equation

A simple sketch graph shows that the root is somewhere around , so taking this to be our starting value successive substitution gets us the sequence

1.84164, 1.85463, 1.85353, 1.85362, 1.8536237 etc.