What are the solutions to the equation sqrt(2)x=(log_{10}(3))x^2 ?

The solutions to the equation sqrt(2)x=(log_{10}(3))x^2 are x=0,x=(sqrt(2))/(log_{10)(3)}

Find the zeros of sqrt(2)x=(log_{10}(3))x^2

The zeros of sqrt(2)x=(log_{10}(3))x^2 are x=0,x=(sqrt(2))/(log_{10)(3)}

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

x = 0, x = \frac{2}{lo g _{10} ( 3 )}

Decimal Notation

x = 0, x = 2.96405 \dots

Solution steps

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

Move

(lo g_{10} (3)) x^{2}

to the left side

2 x - lo g_{10} (3) x^{2} = 0

Factor

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

x (2 - lo g_{10} (3) x) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 2 - lo g_{10} (3) x = 0

Solve

2 - lo g_{10} (3) x = 0 : x = \frac{2}{lo g _{10} ( 3 )}

The solutions to the quadratic equation are:

x = 0, x = \frac{2}{lo g _{10} ( 3 )}

x^{2} - 3 x = x

1 x^{2} + 1 x - 1 = 0

x = 6 x^{2}

x^{2} + 13 x + 40 = 4

(x - 8) (x - 1) = 0

What are the solutions to the equation sqrt(2)x=(log_{10}(3))x^2 ?
The solutions to the equation sqrt(2)x=(log_{10}(3))x^2 are x=0,x=(sqrt(2))/(log_{10)(3)}
Find the zeros of sqrt(2)x=(log_{10}(3))x^2
The zeros of sqrt(2)x=(log_{10}(3))x^2 are x=0,x=(sqrt(2))/(log_{10)(3)}