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Popular >

4^x= 1/x

Solution

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

Solution

x = \frac{1}{2}

+1

Decimal Notation

x = 0.5

Solution steps

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

Prepare

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

for Lambert form:

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

Rewrite the equation with

2 ln (2) x = u

and

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

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

Rewrite

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

in Lambert form:

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

Solve

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

u = ln (2)

Substitute back

u = 2 ln (2) x,

solve for

x

Solve

2 ln (2) x = ln (2) : x = \frac{1}{2}

x = \frac{1}{2}

Verify Solutions:

x = \frac{1}{2}

True

The solution is

x = \frac{1}{2}

Verify Solutions:

x = \frac{1}{2}

True

The solution is

x = \frac{1}{2}

Popular Examples

7^{x} = \frac{1}{343}

17/327 =e^{-9.22\times 10^{-4}t}

\frac{17}{327} = e^{- 9.22 \times 1 0^{- 4} t}

2^{x+1}+5\times 2^x=28

2^{x + 1} + 5 \times 2^{x} = 28

7^{x} = 77

e^{2x}-e^x-20=0

e^{2 x} - e^{x} - 20 = 0

Frequently Asked Questions (FAQ)

What is the answer to 4^x= 1/x ?
The answer to 4^x= 1/x is x= 1/2
Solve for x: 4^x= 1/x
The solution is x= 1/2