What is the answer to m^{sqrt(m)}= 1/2 ?

The answer to m^{sqrt(m)}= 1/2 is m= 1/16 ,m= 1/4

Solve for m: m^{sqrt(m)}= 1/2

The solution is m= 1/16 ,m= 1/4

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Popular >

m^{sqrt(m)}= 1/2

Solution

m^{m} = \frac{1}{2}

Solution

m = \frac{1}{16}, m = \frac{1}{4}

Decimal Notation

m = 0.0625, m = 0.25

Solution steps

m^{m} = \frac{1}{2}

Prepare

m^{m} = \frac{1}{2}

for Lambert form:

m e^{\frac{l n ( 2 )}{m}} = 1

Rewrite the equation with

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

and

m = \frac{ln ^{2} ( 2 )}{u ^{2}}

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

Solve

(\frac{ln ^{2} ( 2 )}{u ^{2}}) e^{- u} = 1 : u = - 4 ln (2), u = - 2 ln (2), u = 2 W_{0} (\frac{ln ( 2 )}{2})

u = - 4 ln (2), u = - 2 ln (2), u = 2 W_{0} (\frac{ln ( 2 )}{2})

Substitute back

u = - \frac{ln ( 2 )}{m},

solve for

m

Solve

- \frac{ln ( 2 )}{m} = - 4 ln (2) : m = \frac{1}{16}

Solve

- \frac{ln ( 2 )}{m} = - 2 ln (2) : m = \frac{1}{4}

Solve

- \frac{ln ( 2 )}{m} = 2 W_{0} (\frac{ln ( 2 )}{2}) :

No Solution for

m \in R

m = \frac{1}{16}, m = \frac{1}{4}

Verify Solutions:

m = \frac{1}{16}

True

, m = \frac{1}{4}

True

The solutions are

m = \frac{1}{16}, m = \frac{1}{4}

Verify Solutions:

m = \frac{1}{16}

True

, m = \frac{1}{4}

True

The solutions are

m = \frac{1}{16}, m = \frac{1}{4}

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e^x*x-e^x=0

e^{x} \cdot x - e^{x} = 0

e^{-x^2}-0.5=0

e^{- x^{2}} - 0.5 = 0

10=58*e^{-90k}+2

10 = 58 \cdot e^{- 90 k} + 2

xln(e^x)+x=12

x ln (e^{x}) + x = 12

x^{10}=2^x

x^{10} = 2^{x}

Frequently Asked Questions (FAQ)

What is the answer to m^{sqrt(m)}= 1/2 ?
The answer to m^{sqrt(m)}= 1/2 is m= 1/16 ,m= 1/4
Solve for m: m^{sqrt(m)}= 1/2
The solution is m= 1/16 ,m= 1/4