What is the answer to (ln(x))^4-3(ln(x))^2-4=0 ?

The answer to (ln(x))^4-3(ln(x))^2-4=0 is x=e^2,x= 1/(e^2)

Solve for x: (ln(x))^4-3(ln(x))^2-4=0

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

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(ln (x))^{4} - 3 (ln (x))^{2} - 4 = 0

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

Solution steps

(ln (x))^{4} - 3 (ln (x))^{2} - 4 = 0

Rewrite the equation with

ln (x) = u

(u)^{4} - 3 (u)^{2} - 4 = 0

Solve

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

u = 2, u = - 2

Substitute back

u = ln (x),

solve for

x

Solve

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

Solve

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

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

Verify Solutions:

x = e^{2}

True

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

True

The solutions are

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

40 = - 10 lo g_{10} ((1 - x)^{2})

lo g_{2} (x^{3} - 56) = 3

ln (x - 1) + ln (2) = 0

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

lo g_{16} (x) = - 4^{- 1}

What is the answer to (ln(x))^4-3(ln(x))^2-4=0 ?
The answer to (ln(x))^4-3(ln(x))^2-4=0 is x=e^2,x= 1/(e^2)
Solve for x: (ln(x))^4-3(ln(x))^2-4=0
The solution is x=e^2,x= 1/(e^2)