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

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

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

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

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

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}

ln (15 - 2 x) = 2 ln (x)

1 = 3 lo g_{10} (4 x + 10)

lo g_{6} (9 x) - 2 lo g_{6} (2) = 3

lo g_{7} (2 x - 3) = 2

lo g_{10} (x^{2} - x - 10) = 1

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