What is the answer to 2ln(3x^2+1)-13=0 ?

The answer to 2ln(3x^2+1)-13=0 is x=sqrt((e^{13/2)-1)/3},x=-sqrt((e^{13/2)-1)/3}

Solve for x: 2ln(3x^2+1)-13=0

The solution is x=sqrt((e^{13/2)-1)/3},x=-sqrt((e^{13/2)-1)/3}

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2 ln (3 x^{2} + 1) - 13 = 0

x = \frac{e ^{\frac{13}{2}} - 1}{3}, x = - \frac{e ^{\frac{13}{2}} - 1}{3}

Decimal Notation

x = 14.87886 \dots, x = - 14.87886 \dots

Solution steps

2 ln (3 x^{2} + 1) - 13 = 0

Move

13

to the right side

2 ln (3 x^{2} + 1) = 13

Divide both sides by

2

ln (3 x^{2} + 1) = \frac{13}{2}

Apply log rules

3 x^{2} + 1 = e^{\frac{13}{2}}

Solve

3 x^{2} + 1 = e^{\frac{13}{2}} : x = \frac{e ^{\frac{13}{2}} - 1}{3}, x = - \frac{e ^{\frac{13}{2}} - 1}{3}

x = \frac{e ^{\frac{13}{2}} - 1}{3}, x = - \frac{e ^{\frac{13}{2}} - 1}{3}

Verify Solutions:

x = \frac{e ^{\frac{13}{2}} - 1}{3}

True

, x = - \frac{e ^{\frac{13}{2}} - 1}{3}

True

The solutions are

x = \frac{e ^{\frac{13}{2}} - 1}{3}, x = - \frac{e ^{\frac{13}{2}} - 1}{3}

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

lo g_{64} (r) = \frac{1}{3}

lo g_{7} (x + 5) + lo g_{7} (x - 1) = 1

lo g_{16} (N) = \frac{1}{4}

4 lo g_{10} (x + 6) = 0

What is the answer to 2ln(3x^2+1)-13=0 ?
The answer to 2ln(3x^2+1)-13=0 is x=sqrt((e^{13/2)-1)/3},x=-sqrt((e^{13/2)-1)/3}
Solve for x: 2ln(3x^2+1)-13=0
The solution is x=sqrt((e^{13/2)-1)/3},x=-sqrt((e^{13/2)-1)/3}