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

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

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ln(x)-3/(ln(x))=2

ln (x) - \frac{3}{ln ( x )} = 2

x = e^{3}, x = \frac{1}{e}

Decimal Notation

x = 20.08553 \dots, x = 0.36787 \dots

Solution steps

ln (x) - \frac{3}{ln ( x )} = 2

Multiply both sides by

ln (x)

ln (x) ln (x) - \frac{3}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (x) ln (x) - \frac{3}{ln ( x )} ln (x) : ln^{2} (x) - 3

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

Rewrite the equation with

ln (x) = u

u^{2} - 3 = 2 u

Solve

u^{2} - 3 = 2 u : u = 3, u = - 1

u = 3, u = - 1

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 3 : x = e^{3}

Solve

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

x = e^{3}, x = \frac{1}{e}

Verify Solutions:

x = e^{3}

True

, x = \frac{1}{e}

True

The solutions are

x = e^{3}, x = \frac{1}{e}

lo g_{3} (x + 17) - 2 = lo g_{3} (2 x)

4 = \frac{ln ( 2 x )}{ln ( 4 x )}

2 lo g_{2} (x) = 4

t, x = ln (t)

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

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