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Popular >

2=2^x+x-1

Solution

2 = 2^{x} + x - 1

Solution

x = 1

Solution steps

2 = 2^{x} + x - 1

Prepare

2 = 2^{x} + x - 1

for Lambert form:

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

Rewrite the equation with

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

and

x = - \frac{u - 3 ln ( 2 )}{ln ( 2 )}

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

Simplify

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

Rewrite

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

in Lambert form:

e^{u} u = 8 ln (2)

Solve

e^{u} u = 8 ln (2) : u = 2 ln (2)

u = 2 ln (2)

Substitute back

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

solve for

x

Solve

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

x = 1

Graph

Popular Examples

3 e^{3 x + 4} - 8 = e

solvefor x,3^{4x-5}=2^{x+3}solve for

x, 3^{4 x - 5} = 2^{x + 3}

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

5^{x + 3} = (\frac{1}{3})^{3 - x}

3^{1 - 2 x} = 4 x

(1/25)^{2x+3}=125^{9x+8}

(\frac{1}{25})^{2 x + 3} = 12 5^{9 x + 8}

Frequently Asked Questions (FAQ)

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