What is the answer to ln^{(2)}(x^{(3)})=e ?

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

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

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

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

Decimal

x = 1.73251 \dots, x = 0.57719 \dots

Solution steps

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

Rewrite the equation with

ln (x^{3}) = u

u^{2} = e

Solve

u^{2} = e : u = e, u = - e

u = e, u = - e

Substitute back

u = ln (x^{3}),

solve for

x

Solve

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

Solve

ln (x^{3}) = - e : x = \frac{1}{e ^{\frac{e}{3}}}

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

Verify Solutions:

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

True

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

True

The solutions are

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

e^{- 2 l n (x)} = - 2 x

lo g_{6} (7 x) = 4

ln (x - 2) = i n^{12} - in (x + 2)

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

lo g_{2} (lo g_{e} (x)) = 1

What is the answer to ln^{(2)}(x^{(3)})=e ?
The answer to ln^{(2)}(x^{(3)})=e is x=e^{(sqrt(e))/3},x= 1/(e^{(sqrt(e))/3)}