What is the answer to 3*b-e^b=0 ?

The answer to 3*b-e^b=0 is b=-\W_{-1}(-1/3),b=-\W_{0}(-1/3)

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3*b-e^b=0

3 \cdot b - e^{b} = 0

b = - W_{- 1} (- \frac{1}{3}), b = - W_{0} (- \frac{1}{3})

Solution steps

3 b - e^{b} = 0

Prepare

3 \cdot b - e^{b} = 0

for Lambert form:

- 1 = - 3 e^{- b} b

Rewrite the equation with

- b = u

and

b = - u

- 1 = - 3 e^{u} (- u)

Rewrite

- 1 = - 3 e^{u} (- u)

in Lambert form:

e^{u} u = - \frac{1}{3}

Solve

e^{u} u = - \frac{1}{3} : u = W_{- 1} (- \frac{1}{3}), u = W_{0} (- \frac{1}{3})

u = W_{- 1} (- \frac{1}{3}), u = W_{0} (- \frac{1}{3})

Substitute back

u = - b,

solve for

b

Solve

- b = W_{- 1} (- \frac{1}{3}) : b = - W_{- 1} (- \frac{1}{3})

Solve

- b = W_{0} (- \frac{1}{3}) : b = - W_{0} (- \frac{1}{3})

b = - W_{- 1} (- \frac{1}{3}), b = - W_{0} (- \frac{1}{3})

6^{x} = 45

3^{2 x + 1} = 7

\frac{27}{1 + e ^{- x}} = 2

8^{2 x - 1} = \frac{1}{2} 32

What is the answer to 3*b-e^b=0 ?
The answer to 3*b-e^b=0 is b=-\W_{-1}(-1/3),b=-\W_{0}(-1/3)