en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

e^x= k/(x-3)

Solution

e^{x} = \frac{k}{x - 3}

Solution

x = W (\frac{k}{e ^{3}}) + 3

Solution steps

e^{x} = \frac{k}{x - 3}

Prepare

e^{x} = \frac{k}{x - 3}

for Lambert form:

e^{x} (x - 3) = k

Rewrite the equation with

x - 3 = u

and

x = u + 3

e^{(u + 3)} ((u + 3) - 3) = k

Simplify

e^{u + 3} u = k

Rewrite

e^{u + 3} u = k

in Lambert form:

e^{u} u = \frac{k}{e ^{3}}

Solve

e^{u} u = \frac{k}{e ^{3}} : u = W (\frac{k}{e ^{3}})

u = W (\frac{k}{e ^{3}})

Substitute back

u = x - 3,

solve for

x

Solve

x - 3 = W (\frac{k}{e ^{3}}) : x = W (\frac{k}{e ^{3}}) + 3

x = W (\frac{k}{e ^{3}}) + 3

Verify Solutions:

x = W (\frac{k}{e ^{3}}) + 3

True

The solution is

x = W (\frac{k}{e ^{3}}) + 3

Verify Solutions:

x = W (\frac{k}{e ^{3}}) + 3

True

The solution is

x = W (\frac{k}{e ^{3}}) + 3

Popular Examples

2(14)^x=(18)^{2x+5}

2 (14)^{x} = (18)^{2 x + 5}

5^{x} + 5^{1 - x} = 6

solvefor x,9^x-1/(3^y)+2=81 solve for

x, 9^{x} - \frac{1}{3 ^{y}} + 2 = 81

2^2x+1=17.2^x-2^3

2^{2} x + 1 = 17. 2^{x} - 2^{3}

9^{x} + 3^{x} = 90

Frequently Asked Questions (FAQ)

What is the answer to e^x= k/(x-3) ?
The answer to e^x= k/(x-3) is x=\W(k/(e^3))+3