What is the answer to ln(1+x^2)=1+2ln(x) ?

The answer to ln(1+x^2)=1+2ln(x) is x=sqrt(1/(e-1))

Solve for x: ln(1+x^2)=1+2ln(x)

The solution is x=sqrt(1/(e-1))

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ln (1 + x^{2}) = 1 + 2 ln (x)

x = \frac{1}{e - 1}

Decimal Notation

x = 0.76287 \dots

Solution steps

ln (1 + x^{2}) = 1 + 2 ln (x)

Apply log rules

1 + x^{2} = e x^{2}

Solve

1 + x^{2} = e x^{2} : x = \frac{1}{e - 1}, x = - \frac{1}{e - 1}

x = \frac{1}{e - 1}, x = - \frac{1}{e - 1}

Verify Solutions:

x = \frac{1}{e - 1}

True

, x = - \frac{1}{e - 1}

False

The solution is

x = \frac{1}{e - 1}

20 = lo g_{10} (x)

2 lo g_{3} (x) + lo g_{3} (9 x) = 2

lo g_{x + 4} (3 x^{2} + 16) = 2

lo g_{2} (3 x) - 2 = lo g_{2} (2 x - 5)

26 = \frac{40}{lo g _{10} ( x + 1 )}

What is the answer to ln(1+x^2)=1+2ln(x) ?
The answer to ln(1+x^2)=1+2ln(x) is x=sqrt(1/(e-1))
Solve for x: ln(1+x^2)=1+2ln(x)
The solution is x=sqrt(1/(e-1))