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

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

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

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

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

x = 1, x = \frac{1}{e ^{\frac{3}{2}}}, x = e^{\frac{3}{2}}

Decimal

x = 1, x = 0.42062 \dots, x = 2.37744 \dots

Solution steps

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

Multiply both sides by

4

\frac{ln ( x ^{3} )}{4} \cdot 4 = (ln (x))^{3} \cdot 4

Simplify

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

Apply log rules

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

Rewrite the equation with

ln (x) = u

3 u = 4 u^{3}

Solve

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

u = 0, u = - \frac{3}{2}, u = \frac{3}{2}

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 0 : x = 1

Solve

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

Solve

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

x = 1, x = \frac{1}{e ^{\frac{3}{2}}}, x = e^{\frac{3}{2}}

Verify Solutions:

x = 1

True

, x = \frac{1}{e ^{\frac{3}{2}}}

True

, x = e^{\frac{3}{2}}

True

The solutions are

x = 1, x = \frac{1}{e ^{\frac{3}{2}}}, x = e^{\frac{3}{2}}

3 - lo g_{2} (5 x - 2) = 0

lo g_{11} (x) = 2

ln (x (x - 2)) = 0

lo g_{5} (x^{2} - 2 x - 10) = 2

a, - 4 = 2 b + 2 lo g_{a} (2)

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