Thread: 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.

Originally Posted by Melody2

I know the answer is approx 1.8536 (Wolfram alpha)
and I know what the graph

There is no simple solution.
But you need to understand Newton Method.

Thanks Plato,
I think that I do understand Newton's method.
I'll try it that way and see how I go.

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.