What is the answer to log_{2}(x^{log_{2}(x)})=4 ?

The answer to log_{2}(x^{log_{2}(x)})=4 is x=4,x= 1/4

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log_{2}(x^{log_{2}(x)})=4

lo g_{2} (x^{l o g_{2} (x)}) = 4

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

Decimal Notation

x = 4, x = 0.25

Solution steps

lo g_{2} (x^{l o g_{2} (x)}) = 4

Apply exponent rules

lo g_{2} (e^{l o g_{2} (x) l n (x)}) = 4

Rewrite the equation with

e^{l o g_{2} (x) l n (x)} = u

lo g_{2} (u) = 4

Solve

lo g_{2} (u) = 4 : u = 16

u = 16

Substitute back

u = e^{l o g_{2} (x) l n (x)},

solve for

x

Solve

e^{l o g_{2} (x) l n (x)} = 16 : x = 4, x = \frac{1}{4}

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

Verify Solutions:

x = 4

True

, x = \frac{1}{4}

True

The solutions are

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

e^{2 x + 1} = 5

x, 4^{x} = 16 y

2 - 4^{∣ x - 1 ∣} = 0

7 = e^{x}

n, a^{n} = b

What is the answer to log_{2}(x^{log_{2}(x)})=4 ?
The answer to log_{2}(x^{log_{2}(x)})=4 is x=4,x= 1/4
Solve for x: log_{2}(x^{log_{2}(x)})=4
The solution is x=4,x= 1/4