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Popular >

4e^{2x}+x-4=0

Solution

4 e^{2 x} + x - 4 = 0

Solution

x = 0

Solution steps

4 e^{2 x} + x - 4 = 0

Prepare

4 e^{2 x} + x - 4 = 0

for Lambert form:

4 = - e^{- 2 x} (x - 4)

Rewrite the equation with

- 2 x + 8 = u

and

x = - \frac{u - 8}{2}

4 = - e^{- 2 (- \frac{u - 8}{2})} ((- \frac{u - 8}{2}) - 4)

Simplify

4 = - e^{u - 8} (- \frac{u - 8}{2} - 4)

Rewrite

4 = - e^{u - 8} (- \frac{u - 8}{2} - 4)

in Lambert form:

e^{u} u = 8 e^{8}

Solve

e^{u} u = 8 e^{8} : u = 8

u = 8

Substitute back

u = - 2 x + 8,

solve for

x

Solve

- 2 x + 8 = 8 : x = 0

x = 0

Popular Examples

3^{x-1}= 1/(sqrt(3))

3^{x - 1} = \frac{1}{3}

-xe^{-x}+9e^{-x}=0

- x e^{- x} + 9 e^{- x} = 0

e^{-36x}-e^{-39x}=0.025e^{-33x}

e^{- 36 x} - e^{- 39 x} = 0.025 e^{- 33 x}

9\times e^{2z}=54

9 \times e^{2 z} = 54

log_{2}(5^{2x}+3)=5

lo g_{2} (5^{2 x} + 3) = 5

Frequently Asked Questions (FAQ)

What is the answer to 4e^{2x}+x-4=0 ?
The answer to 4e^{2x}+x-4=0 is x=0