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Popular >

g(4)=3e^t-2t

Solution

g (4) = 3 e^{t} - 2 t

Solution

t = - W (- \frac{3}{2 e ^{2 g}}) - 2 g

Solution steps

g (4) = 3 e^{t} - 2 t

Prepare

g (4) = 3 e^{t} - 2 t

for Lambert form:

3 = (g \cdot 4 + 2 t) e^{- t}

Rewrite the equation with

- t - 2 g = u

and

t = - u - 2 g

3 = (g \cdot 4 + 2 (- u - 2 g)) e^{- (- u - 2 g)}

Simplify

3 = - 2 e^{u + 2 g} u

Rewrite

3 = - 2 e^{u + 2 g} u

in Lambert form:

e^{u} u = - \frac{3}{2 e ^{2 g}}

Solve

e^{u} u = - \frac{3}{2 e ^{2 g}} : u = W (- \frac{3}{2 e ^{2 g}})

u = W (- \frac{3}{2 e ^{2 g}})

Substitute back

u = - t - 2 g,

solve for

t

Solve

- t - 2 g = W (- \frac{3}{2 e ^{2 g}}) : t = - W (- \frac{3}{2 e ^{2 g}}) - 2 g

t = - W (- \frac{3}{2 e ^{2 g}}) - 2 g

Popular Examples

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2^{2 x + 1} = 50

Frequently Asked Questions (FAQ)

What is the answer to g(4)=3e^t-2t ?
The answer to g(4)=3e^t-2t is t=-\W(-3/(2e^{2g)})-2g