What is the answer to (ln(x))^2-2ln(x^3)=-5 ?

The answer to (ln(x))^2-2ln(x^3)=-5 is x=e^5,x=e

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(ln(x))^2-2ln(x^3)=-5

(ln (x))^{2} - 2 ln (x^{3}) = - 5

x = e^{5}, x = e

Decimal Notation

x = 148.41315 \dots, x = 2.71828 \dots

Solution steps

(ln (x))^{2} - 2 ln (x^{3}) = - 5

Apply log rules

(ln (x))^{2} - 2 \cdot 3 ln (x) = - 5

Rewrite the equation with

ln (x) = u

(u)^{2} - 2 \cdot 3 u = - 5

Solve

u^{2} - 2 \cdot 3 u = - 5 : u = 5, u = 1

u = 5, u = 1

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 5 : x = e^{5}

Solve

ln (x) = 1 : x = e

x = e^{5}, x = e

Verify Solutions:

x = e^{5}

True

, x = e

True

The solutions are

x = e^{5}, x = e

2 lo g_{x} (3 x - 1) = lo g_{x} (4 x)

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

x, lo g_{2} (6 x + 3) = 5

lo g_{x + 5} (4 x) = 3

lo g_{3} (a) = 2

What is the answer to (ln(x))^2-2ln(x^3)=-5 ?
The answer to (ln(x))^2-2ln(x^3)=-5 is x=e^5,x=e
Solve for x: (ln(x))^2-2ln(x^3)=-5
The solution is x=e^5,x=e