What is the answer to (ln(x))^2-ln(x^3)-10=0 ?

The answer to (ln(x))^2-ln(x^3)-10=0 is x=e^5,x= 1/(e^2)

Solve for x: (ln(x))^2-ln(x^3)-10=0

The solution is x=e^5,x= 1/(e^2)

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(ln (x))^{2} - ln (x^{3}) - 10 = 0

x = e^{5}, x = \frac{1}{e ^{2}}

Decimal Notation

x = 148.41315 \dots, x = 0.13533 \dots

Solution steps

(ln (x))^{2} - ln (x^{3}) - 10 = 0

Apply log rules

(ln (x))^{2} - 3 ln (x) - 10 = 0

Rewrite the equation with

ln (x) = u

(u)^{2} - 3 u - 10 = 0

Solve

u^{2} - 3 u - 10 = 0 : u = 5, u = - 2

u = 5, u = - 2

Substitute back

u = ln (x),

solve for

x

Solve

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

Solve

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

x = e^{5}, x = \frac{1}{e ^{2}}

Verify Solutions:

x = e^{5}

True

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

True

The solutions are

x = e^{5}, x = \frac{1}{e ^{2}}

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

x, z = ln (x^{2} y)

lo g_{2} ((4 x + 6)^{2}) = 4

0.324 - ln (\frac{T}{303.15}) = 0

lo g_{\frac{3}{5}} (x) = - 3

What is the answer to (ln(x))^2-ln(x^3)-10=0 ?
The answer to (ln(x))^2-ln(x^3)-10=0 is x=e^5,x= 1/(e^2)
Solve for x: (ln(x))^2-ln(x^3)-10=0
The solution is x=e^5,x= 1/(e^2)