What is the answer to (ln(x))^2-14=5ln(x) ?

The answer to (ln(x))^2-14=5ln(x) is x=e^7,x= 1/(e^2)

Solve for x: (ln(x))^2-14=5ln(x)

The solution is x=e^7,x= 1/(e^2)

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(ln (x))^{2} - 14 = 5 ln (x)

x = e^{7}, x = \frac{1}{e ^{2}}

Decimal Notation

x = 1096.63315 \dots, x = 0.13533 \dots

Solution steps

(ln (x))^{2} - 14 = 5 ln (x)

Rewrite the equation with

ln (x) = u

(u)^{2} - 14 = 5 u

Solve

u^{2} - 14 = 5 u : u = 7, u = - 2

u = 7, u = - 2

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 7 : x = e^{7}

Solve

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

x = e^{7}, x = \frac{1}{e ^{2}}

Verify Solutions:

x = e^{7}

True

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

True

The solutions are

x = e^{7}, x = \frac{1}{e ^{2}}

3.82 = - lo g_{10} (x)

x^{2} ln (x) = 0

lo g_{6} (x) - lo g_{6} (x + 1) = 2

4 lo g_{10} (2 x - 2) = 2

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

What is the answer to (ln(x))^2-14=5ln(x) ?
The answer to (ln(x))^2-14=5ln(x) is x=e^7,x= 1/(e^2)
Solve for x: (ln(x))^2-14=5ln(x)
The solution is x=e^7,x= 1/(e^2)