What is the answer to log^2_{2}(x)+3log_{2}(x)-4=0 ?

The answer to log^2_{2}(x)+3log_{2}(x)-4=0 is x=2,x= 1/16

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log^2_{2}(x)+3log_{2}(x)-4=0

lo g_{2}^{2} (x) + 3 lo g_{2} (x) - 4 = 0

x = 2, x = \frac{1}{16}

Decimal

x = 2, x = 0.0625

Solution steps

lo g_{2}^{2} (x) + 3 lo g_{2} (x) - 4 = 0

Rewrite the equation with

lo g_{2} (x) = u

u^{2} + 3 u - 4 = 0

Solve

u^{2} + 3 u - 4 = 0 : u = 1, u = - 4

u = 1, u = - 4

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

lo g_{2} (x) = 1 : x = 2

Solve

lo g_{2} (x) = - 4 : x = \frac{1}{16}

x = 2, x = \frac{1}{16}

Verify Solutions:

x = 2

True

, x = \frac{1}{16}

True

The solutions are

x = 2, x = \frac{1}{16}

lo g_{2} (x^{4}) = 32

lo g_{2} (x) B

lo g_{3} (x^{3}) = 0

lo g_{x} (5) = 0.7

lo g_{6} (2 x^{2} - 8 x + 12) = 2

What is the answer to log^2_{2}(x)+3log_{2}(x)-4=0 ?
The answer to log^2_{2}(x)+3log_{2}(x)-4=0 is x=2,x= 1/16
Solve for x: log^2_{2}(x)+3log_{2}(x)-4=0
The solution is x=2,x= 1/16