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

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

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

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

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

Decimal Notation

x = 2.71828 \dots, x = 0.04978 \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 = 1, u = - 3

u = 1, u = - 3

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 1 : x = e

Solve

ln (x) = - 3 : x = \frac{1}{e ^{3}}

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

Verify Solutions:

x = e

True

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

True

The solutions are

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

lo g_{e} (x) = 0

lo g_{x} (\frac{1}{64}) = - 2

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

lo g_{6} ((5 x - 9)^{2}) = 4

lo g_{x} (5) = 3

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