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Popular >

5+e^q=-q/2+2

Solution

5 + e^{q} = - \frac{q}{2} + 2

Solution

q = - W_{0} (\frac{2}{e ^{6}}) - 6

+1

Decimal Notation

q = - 6.00493 \dots

Solution steps

5 + e^{q} = - \frac{q}{2} + 2

Prepare

5 + e^{q} = - \frac{q}{2} + 2

for Lambert form:

2 = (- q - 6) e^{- q}

Rewrite the equation with

- q - 6 = u

and

q = - u - 6

2 = (- (- u - 6) - 6) e^{- (- u - 6)}

Simplify

2 = e^{u + 6} u

Rewrite

2 = e^{u + 6} u

in Lambert form:

e^{u} u = \frac{2}{e ^{6}}

Solve

e^{u} u = \frac{2}{e ^{6}} : u = W_{0} (\frac{2}{e ^{6}})

u = W_{0} (\frac{2}{e ^{6}})

Substitute back

u = - q - 6,

solve for

q

Solve

- q - 6 = W_{0} (\frac{2}{e ^{6}}) : q = - W_{0} (\frac{2}{e ^{6}}) - 6

q = - W_{0} (\frac{2}{e ^{6}}) - 6

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5600000 = (1.2)^{t} \cdot 800000

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3(9^x)-26(3^x)-9=0

3 (9^{x}) - 26 (3^{x}) - 9 = 0

x 6^{x - 8} = 7

3^{2x-3}=27(x+1)/3

3^{2 x - 3} = 27 \frac{x + 1}{3}

Frequently Asked Questions (FAQ)

What is the answer to 5+e^q=-q/2+2 ?
The answer to 5+e^q=-q/2+2 is q=-\W_{0}(2/(e^6))-6