What is the answer to (ln(x))^2= 1/(3ln(x)) ?

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

Solve for x: (ln(x))^2= 1/(3ln(x))

The solution is x=e^{\sqrt[3]{1/3}}

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(ln (x))^{2} = \frac{1}{3 ln ( x )}

Decimal Notation

x = 2.00042 \dots

Solution steps

(ln (x))^{2} = \frac{1}{3 ln ( x )}

Multiply both sides by

3 ln (x)

(ln (x))^{2} \cdot 3 ln (x) = \frac{1}{3 ln ( x )} \cdot 3 ln (x)

Simplify

ln^{2} (x) \cdot 3 ln (x) : 3 ln^{3} (x)

3 ln^{3} (x) = 1

Rewrite the equation with

ln (x) = u

3 u^{3} = 1

Solve

Substitute back

u = ln (x),

solve for

x

Solve

Verify Solutions:

True

The solution is

0.46 = ln (y)

6.9 = lo g_{10} (6.9 x^{1})

3 ln (x + 7) = 6

x + ln (x) = 1

36 = lo g_{2} (x)

What is the answer to (ln(x))^2= 1/(3ln(x)) ?
The answer to (ln(x))^2= 1/(3ln(x)) is x=e^{\sqrt[3]{1/3}}
Solve for x: (ln(x))^2= 1/(3ln(x))
The solution is x=e^{\sqrt[3]{1/3}}