What is the answer to 2ln(x)=(ln(x))^{-1}+1 ?

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

Solve for x: 2ln(x)=(ln(x))^{-1}+1

The solution is x=e,x= 1/(sqrt(e))

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

x = e, x = \frac{1}{e}

Decimal Notation

x = 2.71828 \dots, x = 0.60653 \dots

Solution steps

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

Rewrite the equation with

ln (x) = u

2 u = (u)^{- 1} + 1

Solve

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

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

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 1 : x = e

Solve

ln (x) = - \frac{1}{2} : x = \frac{1}{e}

x = e, x = \frac{1}{e}

Verify Solutions:

x = e

True

, x = \frac{1}{e}

True

The solutions are

x = e, x = \frac{1}{e}

lo g_{2} (y) = 2

lo g_{2} (x) = 2 + lo g_{8} (x)

ln (2 x) = 5 x

ln (x) + ln (x + 2) = 3 \cdot ln (2)

72 = lo g_{10} (x)

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