What is the answer to log^2_{2}(x)-log_{2}(x)=2 ?

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

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log^2_{2}(x)-log_{2}(x)=2

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

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

Decimal Notation

x = 4, x = 0.5

Solution steps

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

Rewrite the equation with

lo g_{2} (x) = u

u^{2} - u = 2

Solve

u^{2} - 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}

lo g_{2} (x + 1) = 5

lo g_{x} (5) + lo g_{x} (12) = 7

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

lo g_{10} (x) + lo g_{10} (x - 7) = 2

lo g_{2} (x) + lo g_{4} (x) = 3

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