solvefor x,e^x=lnx

Lösung

löse nach

x, e^{x} = ln (x)

Keine L \overset{o}{¨} sung

Schritte zur Lösung

e^{x} = ln (x)

Find the difference function

f (x) = e^{x} - ln (x)

Look for the function's extreme points

Extrempunkte vonf

e^{x} - ln (x), x > 0 :

Minimum

(0.56714 \dots, 2.33036 \dots)

Check function behavior at domain edges:

0, \infty

x \to 0 + lim (e^{x} - ln (x)) = \infty

x \to \infty lim (e^{x} - ln (x)) = \infty

The interval between every consecutive point pair is monotone

x f (x) 0.56714 \dots 2.33036 \dots \infty \infty

Check every interval, if the signs at the edges are different, find the X intersection using Brent method

Points

(0, 2.33036 \dots)

and

(\infty, \infty)

have the same sign, no solution in this interval

= Keine L \overset{o}{¨} sung