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

The answer to x=ln(x)+2 is x=-\W_{-1}(-1/(e^2)),x=-\W_{0}(-1/(e^2))

Solve for x: x=ln(x)+2

The solution is x=-\W_{-1}(-1/(e^2)),x=-\W_{0}(-1/(e^2))

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x = ln (x) + 2

x = - W_{- 1} (- \frac{1}{e ^{2}}), x = - W_{0} (- \frac{1}{e ^{2}})

Decimal Notation

x = 3.14619 \dots, x = 0.15859 \dots

Solution steps

x = ln (x) + 2

Switch sides

ln (x) + 2 = x

Move

2

to the right side

ln (x) = x - 2

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

e^{l n (x)} = e^{x - 2}

Simplify

e^{l n (x)} : x

x = e^{x - 2}

Solve

x = e^{x - 2} : x = - W_{- 1} (- \frac{1}{e ^{2}}), x = - W_{0} (- \frac{1}{e ^{2}})

x = - W_{- 1} (- \frac{1}{e ^{2}}), x = - W_{0} (- \frac{1}{e ^{2}})

Verify Solutions:

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

True

, x = - W_{0} (- \frac{1}{e ^{2}})

True

The solutions are

x = - W_{- 1} (- \frac{1}{e ^{2}}), x = - W_{0} (- \frac{1}{e ^{2}})

lo g_{7} (x^{3} - 3 x^{2} + 3 x - 1) = 6

3 ln (2 x) = 15

3 ln (2 x) = 12

3 ln (5 x - 1) + 17 = 29

lo g_{5} (x + 2) + lo g_{5} (x) = 1.5

What is the answer to x=ln(x)+2 ?
The answer to x=ln(x)+2 is x=-\W_{-1}(-1/(e^2)),x=-\W_{0}(-1/(e^2))
Solve for x: x=ln(x)+2
The solution is x=-\W_{-1}(-1/(e^2)),x=-\W_{0}(-1/(e^2))