What is the answer to -3x+2=4^x+2 ?

The answer to -3x+2=4^x+2 is x=-(\W_{0}((2ln(2))/3))/(2ln(2))

Solve for x: -3x+2=4^x+2

The solution is x=-(\W_{0}((2ln(2))/3))/(2ln(2))

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

x = - \frac{W _{0} ( \frac{2 l n ( 2 )}{3} )}{2 ln ( 2 )}

Decimal Notation

x = - 0.23924 \dots

Solution steps

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

Prepare

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

for Lambert form:

1 = - 3 e^{- 2 l n (2) x} x

Rewrite the equation with

- 2 ln (2) x = u

and

x = - \frac{u}{2 ln ( 2 )}

1 = - 3 e^{u} (- \frac{u}{2 ln ( 2 )})

Rewrite

1 = - 3 e^{u} (- \frac{u}{2 ln ( 2 )})

in Lambert form:

e^{u} u = \frac{2 ln ( 2 )}{3}

Solve

e^{u} u = \frac{2 ln ( 2 )}{3} : u = W_{0} (\frac{2 ln ( 2 )}{3})

u = W_{0} (\frac{2 ln ( 2 )}{3})

Substitute back

u = - 2 ln (2) x,

solve for

x

Solve

- 2 ln (2) x = W_{0} (\frac{2 ln ( 2 )}{3}) : x = - \frac{W _{0} ( \frac{2 l n ( 2 )}{3} )}{2 ln ( 2 )}

x = - \frac{W _{0} ( \frac{2 l n ( 2 )}{3} )}{2 ln ( 2 )}

e^{5 k} = (32)

e^{- 6 x} = 1 - 4 x

z, c = e^{2 x + 2 y + z}

3^{x + 2} - 3^{x + 1} + 3^{x} = 63

3^{x + 4} = 9

What is the answer to -3x+2=4^x+2 ?
The answer to -3x+2=4^x+2 is x=-(\W_{0}((2ln(2))/3))/(2ln(2))
Solve for x: -3x+2=4^x+2
The solution is x=-(\W_{0}((2ln(2))/3))/(2ln(2))