What is the answer to (ln(x))^2-3ln(x^4)=28 ?

The answer to (ln(x))^2-3ln(x^4)=28 is x=e^{14},x= 1/(e^2)

Solve for x: (ln(x))^2-3ln(x^4)=28

The solution is x=e^{14},x= 1/(e^2)

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(ln (x))^{2} - 3 ln (x^{4}) = 28

x = e^{14}, x = \frac{1}{e ^{2}}

Decimal Notation

x = 1202604.28416 \dots, x = 0.13533 \dots

Solution steps

(ln (x))^{2} - 3 ln (x^{4}) = 28

Apply log rules

(ln (x))^{2} - 3 \cdot 4 ln (x) = 28

Rewrite the equation with

ln (x) = u

(u)^{2} - 3 \cdot 4 u = 28

Solve

u^{2} - 3 \cdot 4 u = 28 : u = 14, u = - 2

u = 14, u = - 2

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 14 : x = e^{14}

Solve

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

x = e^{14}, x = \frac{1}{e ^{2}}

Verify Solutions:

x = e^{14}

True

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

True

The solutions are

x = e^{14}, x = \frac{1}{e ^{2}}

lo g_{10} (x + 1) = 2

3 x + 2 y = 11, 2 x - y = 5

5 x + 2 y = 1, - 3 x + 3 y = 5

- 4 x + 2 y = - 60, - 2 x - 6 y = 12

3 x - 2 y = 12, 3 x + 2 y = 0

What is the answer to (ln(x))^2-3ln(x^4)=28 ?
The answer to (ln(x))^2-3ln(x^4)=28 is x=e^{14},x= 1/(e^2)
Solve for x: (ln(x))^2-3ln(x^4)=28
The solution is x=e^{14},x= 1/(e^2)