What is the answer to (ln(x))^3=7ln(x) ?

The answer to (ln(x))^3=7ln(x) is x=1,x= 1/(e^{sqrt(7))},x=e^{sqrt(7)}

Solve for x: (ln(x))^3=7ln(x)

The solution is x=1,x= 1/(e^{sqrt(7))},x=e^{sqrt(7)}

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(ln (x))^{3} = 7 ln (x)

x = 1, x = \frac{1}{e ^{7}}, x = e^{7}

Solution steps

(ln (x))^{3} = 7 ln (x)

Rewrite the equation with

ln (x) = u

(u)^{3} = 7 u

Solve

u^{3} = 7 u : u = 0, u = - 7, u = 7

u = 0, u = - 7, u = 7

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 0 : x = 1

Solve

ln (x) = - 7 : x = \frac{1}{e ^{7}}

Solve

ln (x) = 7 : x = e^{7}

x = 1, x = \frac{1}{e ^{7}}, x = e^{7}

Verify Solutions:

x = 1

True

, x = \frac{1}{e ^{7}}

True

, x = e^{7}

True

The solutions are

x = 1, x = \frac{1}{e ^{7}}, x = e^{7}

lo g_{4} (100 - 3 x) = 23219

6 = lo g_{10} (x)

x, - 5 lo g_{3} (2 x) = - 5

1 + lo g_{\frac{1}{2}} (x) = 0

1 + lo g_{\frac{1}{2}} (x) = 1

What is the answer to (ln(x))^3=7ln(x) ?
The answer to (ln(x))^3=7ln(x) is x=1,x= 1/(e^{sqrt(7))},x=e^{sqrt(7)}
Solve for x: (ln(x))^3=7ln(x)
The solution is x=1,x= 1/(e^{sqrt(7))},x=e^{sqrt(7)}