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Popular >

x=e^{((xln(2)))/2}

Solution

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

Solution

x = 4, x = 2

Solution steps

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

Prepare

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

for Lambert form:

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

Rewrite the equation with

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

and

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

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

Rewrite

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

in Lambert form:

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

Solve

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

u = - 2 ln (2), u = - ln (2)

Substitute back

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

solve for

x

Solve

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

Solve

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

x = 4, x = 2

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2500 = 5000 e^{100 x}

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3^{3 x - 7} = \frac{1}{81}

1.0 4^{n} = 1.28858

Frequently Asked Questions (FAQ)

What is the answer to x=e^{((xln(2)))/2} ?
The answer to x=e^{((xln(2)))/2} is x=4,x=2