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

The answer to 2^x=4x 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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2^x=4x

2^{x} = 4 x

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

Decimal Notation

x = 4, x = 0.30990 \dots

Solution steps

2^{x} = 4 x

Prepare

2^{x} = 4 x

for Lambert form:

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

Rewrite the equation with

- x ln (2) = u

and

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

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

Simplify

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

Rewrite

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

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 )}

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

8 (e)^{2 x + 1} = 4

0 = 2^{x} - 1

100 0^{3 x - 2} = 1

5^{x + 2} = 7^{x - 2}

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