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

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

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

The solution is x=e^{2/3},x= 1/e

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

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

Decimal

x = 1.94773 \dots, x = 0.36787 \dots

Solution steps

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

Rewrite the equation with

ln (x) = u

3 u^{2} + u = 2

Solve

3 u^{2} + u = 2 : u = \frac{2}{3}, u = - 1

u = \frac{2}{3}, u = - 1

Substitute back

u = ln (x),

solve for

x

Solve

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

Solve

ln (x) = - 1 : x = \frac{1}{e}

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

Verify Solutions:

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

True

, x = \frac{1}{e}

True

The solutions are

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

5 = ln (x)

ln (x - 2) = 3

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

lo g_{10} (x) + lo g_{10} (x + 9) = 1

lo g_{y} (4826809) = 6

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