Question

what is z?
z +ln z = 1+e

Answer 1

wolfram said you cant solve it algebraically, and i dont see a way to anyways.....

Answer 2

I think i might know...

\[e(z+\ln z=1+e)\]
\[ze + z = e + e^2\]
\[z(e+1) = e+e^2\]
\[z = \frac{ e+e^2 }{ e+1 }\]

Can someone verify me? I took a shot at it.

Answer 3

but eln(z) is not equal to z, your mistaking e^ln(z)

Answer 4

e^ln(4) = 4 BUT if e*ln(4) does not equal 4

Answer 5

if \(z = e\), then \(\ln z = 1\)


"a" solution

Answer 6

There is NOT a closed-form, expression that represents an algebraic solution. There is a numerical solution, as suggested by IrishBoy123. z + ln(z) is monotonic increasing, so we will not be finding another solution.

Answer 7

@iTz_Sid
If you multiply e to the equation, then the second guy is elnz = ln z^e, not = z

Answer 8

Newton's Method would help you to find one or more roots of z +ln z = 1+e.

If you know this Method, start out by forming the new function f(z)=z+ln z-1-e.