What is the answer to (ln(x))^3=ln(x^4) ?

The answer to (ln(x))^3=ln(x^4) is x=1,x= 1/(e^2),x=e^2

Solve for x: (ln(x))^3=ln(x^4)

The solution is x=1,x= 1/(e^2),x=e^2

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(ln (x))^{3} = ln (x^{4})

x = 1, x = \frac{1}{e ^{2}}, x = e^{2}

Decimal Notation

x = 1, x = 0.13533 \dots, x = 7.38905 \dots

Solution steps

(ln (x))^{3} = ln (x^{4})

Apply log rules

(ln (x))^{3} = 4 ln (x)

Rewrite the equation with

ln (x) = u

(u)^{3} = 4 u

Solve

u^{3} = 4 u : u = 0, u = - 2, u = 2

u = 0, u = - 2, u = 2

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 0 : x = 1

Solve

ln (x) = - 2 : x = \frac{1}{e ^{2}}

Solve

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

x = 1, x = \frac{1}{e ^{2}}, x = e^{2}

Verify Solutions:

x = 1

True

, x = \frac{1}{e ^{2}}

True

, x = e^{2}

True

The solutions are

x = 1, x = \frac{1}{e ^{2}}, x = e^{2}

lo g_{9} (x) = 4

lo g_{9} (x) = 1

lo g_{2} (x + 2) = lo g_{3} (27)

lo g_{x} (625) = 2

lo g_{5} (3 x - 1) = lo g_{5} (23)

What is the answer to (ln(x))^3=ln(x^4) ?
The answer to (ln(x))^3=ln(x^4) is x=1,x= 1/(e^2),x=e^2
Solve for x: (ln(x))^3=ln(x^4)
The solution is x=1,x= 1/(e^2),x=e^2