What is the answer to ln(3-x^2)=2ln(x) ?

The answer to ln(3-x^2)=2ln(x) is x=sqrt(3/2)

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ln(3-x^2)=2ln(x)

ln (3 - x^{2}) = 2 ln (x)

x = \frac{3}{2}

Decimal Notation

x = 1.22474 \dots

Solution steps

ln (3 - x^{2}) = 2 ln (x)

Apply log rules

3 - x^{2} = x^{2}

Solve

3 - x^{2} = x^{2} : x = \frac{3}{2}, x = - \frac{3}{2}

x = \frac{3}{2}, x = - \frac{3}{2}

Verify Solutions:

x = \frac{3}{2}

True

, x = - \frac{3}{2}

False

The solution is

x = \frac{3}{2}

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

2 x \cdot ln (x) + x = 0

lo g_{2} (3 x - 1) = lo g_{4} (x + 8)

0.79 = lo g_{10} (x)

0 = lo g_{2} (x)

What is the answer to ln(3-x^2)=2ln(x) ?
The answer to ln(3-x^2)=2ln(x) is x=sqrt(3/2)
Solve for x: ln(3-x^2)=2ln(x)
The solution is x=sqrt(3/2)