What is the answer to x-50e^{(-x/(200))}=175 ?

The answer to x-50e^{(-x/(200))}=175 is x=200\W_{0}(1/(4e^{7/8)})+175

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x-50e^{(-x/(200))}=175

x - 50 e^{(- \frac{x}{200})} = 175

x = 200 W_{0} (\frac{1}{4 e ^{\frac{7}{8}}}) + 175

Solution steps

x - 50 e^{(- \frac{x}{200})} = 175

Prepare

x - 50 e^{(- \frac{x}{200})} = 175

for Lambert form:

- 50 = (175 - x) e^{\frac{x}{200}}

Rewrite the equation with

\frac{1}{200} x - \frac{7}{8} = u

and

x = 200 u + 175

- 50 = (175 - (200 u + 175)) e^{\frac{( 200 u + 175 )}{200}}

Simplify

- 50 = - 200 e^{\frac{8 u + 7}{8}} u

Rewrite

- 50 = - 200 e^{\frac{8 u + 7}{8}} u

in Lambert form:

e^{u} u = \frac{1}{4 e ^{\frac{7}{8}}}

Solve

e^{u} u = \frac{1}{4 e ^{\frac{7}{8}}} : u = W_{0} (\frac{1}{4 e ^{\frac{7}{8}}})

u = W_{0} (\frac{1}{4 e ^{\frac{7}{8}}})

Substitute back

u = \frac{1}{200} x - \frac{7}{8},

solve for

x

Solve

\frac{1}{200} x - \frac{7}{8} = W_{0} (\frac{1}{4 e ^{\frac{7}{8}}}) : x = 200 W_{0} (\frac{1}{4 e ^{\frac{7}{8}}}) + 175

x = 200 W_{0} (\frac{1}{4 e ^{\frac{7}{8}}}) + 175

ln (1 + x^{x}) = 0

a^{x - 5} = a

4^{- x} = 2^{x^{2} + 2 x - 8}

y, x = 2 e^{(3 y)}

2 3^{9} - 2 3^{8} = 22 \cdot 2 3^{x}

What is the answer to x-50e^{(-x/(200))}=175 ?
The answer to x-50e^{(-x/(200))}=175 is x=200\W_{0}(1/(4e^{7/8)})+175