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

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

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

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

x = 4, x = \frac{1}{2}

Decimal

x = 4, x = 0.5

Solution steps

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

Apply log rules

lo g_{2} (x) lo g_{2} (x) = lo g_{2} (x) + 2

Rewrite the equation with

lo g_{2} (x) = u

uu = u + 2

Solve

uu = u + 2 : u = 2, u = - 1

u = 2, u = - 1

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

lo g_{2} (x) = 2 : x = 4

Solve

lo g_{2} (x) = - 1 : x = \frac{1}{2}

x = 4, x = \frac{1}{2}

Verify Solutions:

x = 4

True

, x = \frac{1}{2}

True

The solutions are

x = 4, x = \frac{1}{2}

2 lo g_{10} (x - 1) = 0

lo g_{7} (x^{2} - 2 x - 8) = 1

lo g_{2} (x^{2} - 3 x + 10) = 3

lo g_{3} (x + 3) = 2

lo g_{5} (3 x + 5) = 3

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