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

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

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

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

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

Solution steps

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

lo g_{6} (16) = 4 lo g_{6} (x)

lo g_{16} (r) = \frac{1}{4}

x, ln (y) = - ln (x) + C

e^{- \frac{2}{3}} + 15 - 10 = ln (c)

5 lo g_{3} (4 x - 3) = 10

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