What is the answer to 4x=2^x ?

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

The solution is x=4,x=-(\W_{0}(-(ln(2))/4))/(ln(2))

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4x=2^x

4 x = 2^{x}

x = 4, x = - \frac{W _{0} ( - \frac{l n ( 2 )}{4} )}{ln ( 2 )}

Decimal Notation

x = 4, x = 0.30990 \dots

Solution steps

4 x = 2^{x}

Prepare

4 x = 2^{x}

for Lambert form:

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

Rewrite the equation with

- x ln (2) = u

and

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

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

Simplify

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

Rewrite

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

in Lambert form:

e^{u} u = - \frac{ln ( 2 )}{4}

Solve

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

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

Substitute back

u = - x ln (2),

solve for

x

Solve

- x ln (2) = - 4 ln (2) : x = 4

Solve

- x ln (2) = W_{0} (- \frac{ln ( 2 )}{4}) : x = - \frac{W _{0} ( - \frac{l n ( 2 )}{4} )}{ln ( 2 )}

x = 4, x = - \frac{W _{0} ( - \frac{l n ( 2 )}{4} )}{ln ( 2 )}

x, [t] = [p^{x} \cdot d^{y} \cdot e^{2}]

5^{6 x + 8} = 12 5^{4}

(- 4)^{x} = 1024

2^{a - 2} + 2^{3 - a} = 3

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

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