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Popular >

x^{2x}=16

Solution

x^{2 x} = 16

Solution

x = 2

Solution steps

x^{2 x} = 16

Prepare

x^{2 x} = 16

for Lambert form:

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

Rewrite the equation with

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

and

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

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

Rewrite

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

in Lambert form:

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

Solve

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

Verify Solutions:

u = ln (2)

True

The solution is

u = ln (2)

Substitute back

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

solve for

x

Solve

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

x = 2

Popular Examples

4^{x+2}*8^{3x+1}=64

4^{x + 2} \cdot 8^{3 x + 1} = 64

1 0^{x} = 45

1 0^{x} = 41

x e^{x} = e^{x}

2^{2x+1}-3*2^x-2=0

2^{2 x + 1} - 3 \cdot 2^{x} - 2 = 0

Frequently Asked Questions (FAQ)

What is the answer to x^{2x}=16 ?
The answer to x^{2x}=16 is x=2
Solve for x: x^{2x}=16
The solution is x=2