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

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

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

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

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

Decimal Notation

x = 2.71828 \dots, x = 0.13533 \dots

Solution steps

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

Multiply both sides by

ln (x)

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

Simplify

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

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

Rewrite the equation with

ln (x) = u

u^{2} = 2 - u

Solve

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

u = 1, u = - 2

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 1 : x = e

Solve

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

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

Verify Solutions:

x = e

True

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

True

The solutions are

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

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

y, ln (y) = 0.85 x + c

ln (x) = 2.0353

50 = 12.036 ln (x) + 2.9211

lo g_{b} (1) = 0

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