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

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

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

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

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

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

Solution steps

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

Rewrite the equation with

ln (x) = u

u + u^{2} = 3

Solve

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

u = \frac{- 1 + 13}{2}, u = \frac{- 1 - 13}{2}

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = \frac{- 1 + 13}{2} : x = e^{\frac{- 1 + 13}{2}}

Solve

ln (x) = \frac{- 1 - 13}{2} : x = e^{\frac{- 1 - 13}{2}}

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

Verify Solutions:

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

True

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

True

The solutions are

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

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ln ((x - 4)^{2}) = 3.219

lo g_{10} (9) (a) = lo g_{3} (x)

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