What is the answer to x^{log_{2}(x)}=64x ?

The answer to x^{log_{2}(x)}=64x is x=8,x= 1/4

Popular >

x^{log_{2}(x)}=64x

x^{l o g_{2} (x)} = 64 x

x = 8, x = \frac{1}{4}

Decimal

x = 8, x = 0.25

Solution steps

x^{l o g_{2} (x)} = 64 x

Apply log rules

lo g_{2} (x) lo g_{2} (x) = lo g_{2} (x) + 6

Rewrite the equation with

lo g_{2} (x) = u

uu = u + 6

Solve

uu = u + 6 : u = 3, u = - 2

u = 3, u = - 2

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

lo g_{2} (x) = 3 : x = 8

Solve

lo g_{2} (x) = - 2 : x = \frac{1}{4}

x = 8, x = \frac{1}{4}

Verify Solutions:

x = 8

True

, x = \frac{1}{4}

True

The solutions are

x = 8, x = \frac{1}{4}

lo g_{2} (x^{2} - 5 x - 4) = 1

lo g_{x} (e) = - 3

lo g_{x} (256) = - 8

lo g_{10} (x) - lo g_{10} (8) = 3

lo g_{10} (x + 12) = lo g_{10} (x) + lo g_{10} (12)

What is the answer to x^{log_{2}(x)}=64x ?
The answer to x^{log_{2}(x)}=64x is x=8,x= 1/4
Solve for x: x^{log_{2}(x)}=64x
The solution is x=8,x= 1/4