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

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

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

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

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

Decimal

u = 4, u = 0.5

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{2} (u) = v

v + 2 = vv

Solve

v + 2 = vv : v = 2, v = - 1

v = 2, v = - 1

Substitute back

v = lo g_{2} (u),

solve for

u

Solve

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

Solve

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

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

Verify Solutions:

u = 4

True

, u = \frac{1}{2}

True

The solutions are

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

x, lo g_{2} (3 x + 5) = z

\frac{2}{3} lo g_{10} (x) = 6

20 lo g_{10} (x) = 6

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

x, ln (y) = ln (x) + c

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