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Popular >

2x+4^x=6

Solution

2 x + 4^{x} = 6

Solution

x = 1

Solution steps

2 x + 4^{x} = 6

Prepare

2 x + 4^{x} = 6

for Lambert form:

1 = (6 - 2 x) e^{- 2 l n (2) x}

Rewrite the equation with

2 ln (2) (- x + 3) = u

and

x = - \frac{u - 6 ln ( 2 )}{2 ln ( 2 )}

1 = (6 - 2 (- \frac{u - 6 ln ( 2 )}{2 ln ( 2 )})) e^{- 2 l n (2) (- \frac{u - 6 l n ( 2 )}{2 l n ( 2 )})}

Simplify

1 = e^{u - 6 l n (2)} (6 + \frac{u - 6 ln ( 2 )}{ln ( 2 )})

Rewrite

1 = e^{u - 6 l n (2)} (6 + \frac{u - 6 ln ( 2 )}{ln ( 2 )})

in Lambert form:

e^{u} u = 64 ln (2)

Solve

e^{u} u = 64 ln (2) : u = 4 ln (2)

u = 4 ln (2)

Substitute back

u = 2 ln (2) (- x + 3),

solve for

x

Solve

2 ln (2) (- x + 3) = 4 ln (2) : x = 1

x = 1

Popular Examples

4^{-2x+2}=16^{x-3}

4^{- 2 x + 2} = 1 6^{x - 3}

25^{x+3}=5^{x+2}

2 5^{x + 3} = 5^{x + 2}

2^{4x}=2^{2x-6}

2^{4 x} = 2^{2 x - 6}

4^{x} = 2^{x} \cdot 2^{x}

2^{x} + 2^{2 - x} = 17

Frequently Asked Questions (FAQ)

What is the answer to 2x+4^x=6 ?
The answer to 2x+4^x=6 is x=1
Solve for x: 2x+4^x=6
The solution is x=1