solvefor x,e^x=lnx

解答

求解

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

无解

求解步骤

e^{x} = ln (x)

Find the difference function

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

Look for the function's extreme points

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

的极值点:

极小值

(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

= 无解

6^{x} - 6^{1 - x} = 1

0. 5^{x} = 128

\frac{2 5 ^{4}}{5 ^{5 y}} = 12 5^{y}

5 \cdot \frac{5 ^{5 x}}{2 5 ^{x}} = 25

roo t s t e^{a t}