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

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

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

The solution is x=1,x= 1/(e^{sqrt(3))},x=e^{sqrt(3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Decimal

x = 1, x = 0.17692 \dots, x = 5.65223 \dots

Solution steps

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

Rewrite the equation with

ln (x) = u

(u)^{3} = 3 u

Solve

u^{3} = 3 u : u = 0, u = - 3, u = 3

u = 0, u = - 3, u = 3

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 0 : x = 1

Solve

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

Solve

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

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

Verify Solutions:

x = 1

True

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

True

, x = e^{3}

True

The solutions are

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

lo g_{4} (x^{2} - x - 5) = 2

lo g_{10} (\frac{x}{0.145}) = - 0.34472

y, x = ln (y - 1) + 2

lo g_{10} (x) + lo g_{10} (x + 3) = 6

lo g_{10} (x) + lo g_{10} (x + 3) = 5

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