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

The answer to ln(x)(2ln(x)+1)=2 is x=e^{(-1+sqrt(17))/4},x=e^{(-1-sqrt(17))/4}

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

The solution is x=e^{(-1+sqrt(17))/4},x=e^{(-1-sqrt(17))/4}

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ln (x) (2 ln (x) + 1) = 2

x = e^{\frac{- 1 + 17}{4}}, x = e^{\frac{- 1 - 17}{4}}

Decimal Notation

x = 2.18316 \dots, x = 0.27782 \dots

Solution steps

ln (x) (2 ln (x) + 1) = 2

Rewrite the equation with

ln (x) = u

u (2 u + 1) = 2

Solve

u (2 u + 1) = 2 : u = \frac{- 1 + 17}{4}, u = \frac{- 1 - 17}{4}

u = \frac{- 1 + 17}{4}, u = \frac{- 1 - 17}{4}

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = \frac{- 1 + 17}{4} : x = e^{\frac{- 1 + 17}{4}}

Solve

ln (x) = \frac{- 1 - 17}{4} : x = e^{\frac{- 1 - 17}{4}}

x = e^{\frac{- 1 + 17}{4}}, x = e^{\frac{- 1 - 17}{4}}

Verify Solutions:

x = e^{\frac{- 1 + 17}{4}}

True

, x = e^{\frac{- 1 - 17}{4}}

True

The solutions are

x = e^{\frac{- 1 + 17}{4}}, x = e^{\frac{- 1 - 17}{4}}

lo g_{2} (n) = 2

lo g_{e} (7 x - 3) = x + 9

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

4 lo g_{9} (x) = 0

lo g_{2} (n) = 3

What is the answer to ln(x)(2ln(x)+1)=2 ?
The answer to ln(x)(2ln(x)+1)=2 is x=e^{(-1+sqrt(17))/4},x=e^{(-1-sqrt(17))/4}
Solve for x: ln(x)(2ln(x)+1)=2
The solution is x=e^{(-1+sqrt(17))/4},x=e^{(-1-sqrt(17))/4}