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

The answer to 3ln(x^2-2)=2 is x=sqrt(e^{2/3)+2},x=-sqrt(e^{2/3)+2}

Solve for x: 3ln(x^2-2)=2

The solution is x=sqrt(e^{2/3)+2},x=-sqrt(e^{2/3)+2}

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

x = e^{\frac{2}{3}} + 2, x = - e^{\frac{2}{3}} + 2

Decimal Notation

x = 1.98689 \dots, x = - 1.98689 \dots

Solution steps

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

Divide both sides by

3

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

Apply log rules

x^{2} - 2 = e^{\frac{2}{3}}

Solve

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

x = e^{\frac{2}{3}} + 2, x = - e^{\frac{2}{3}} + 2

Verify Solutions:

x = e^{\frac{2}{3}} + 2

True

, x = - e^{\frac{2}{3}} + 2

True

The solutions are

x = e^{\frac{2}{3}} + 2, x = - e^{\frac{2}{3}} + 2

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

lo g_{2} (8 x - 3) = lo g_{10} (200)

(ln (x))^{2} - 2 ln (x^{3}) = - 5

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

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

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