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

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

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

The solution is x=sqrt(2/(e-1))

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

x = \frac{2}{e - 1}

Decimal Notation

x = 1.07886 \dots

Solution steps

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

Apply log rules

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

Solve

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

x = \frac{2}{e - 1}, x = - \frac{2}{e - 1}

Verify Solutions:

x = \frac{2}{e - 1}

True

, x = - \frac{2}{e - 1}

False

The solution is

x = \frac{2}{e - 1}

4 lo g_{y} (2) + lo g_{2} (y) = 4

10 lo g_{10} (x) = - 1

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

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

x, ln (x + 1) = 2

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