What is the answer to x=ln(x)+6 ?

The answer to x=ln(x)+6 is x=-\W_{-1}(-1/(e^6)),x=-\W_{0}(-1/(e^6))

Solve for x: x=ln(x)+6

The solution is x=-\W_{-1}(-1/(e^6)),x=-\W_{0}(-1/(e^6))

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x = ln (x) + 6

x = - W_{- 1} (- \frac{1}{e ^{6}}), x = - W_{0} (- \frac{1}{e ^{6}})

Decimal Notation

x = 8.09071 \dots, x = 0.00248 \dots

Solution steps

x = ln (x) + 6

Switch sides

ln (x) + 6 = x

Move

6

to the right side

ln (x) = x - 6

f (x) = g (x),

then

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

e^{l n (x)} = e^{x - 6}

Simplify

e^{l n (x)} : x

x = e^{x - 6}

Solve

x = e^{x - 6} : x = - W_{- 1} (- \frac{1}{e ^{6}}), x = - W_{0} (- \frac{1}{e ^{6}})

x = - W_{- 1} (- \frac{1}{e ^{6}}), x = - W_{0} (- \frac{1}{e ^{6}})

Verify Solutions:

x = - W_{- 1} (- \frac{1}{e ^{6}})

True

, x = - W_{0} (- \frac{1}{e ^{6}})

True

The solutions are

x = - W_{- 1} (- \frac{1}{e ^{6}}), x = - W_{0} (- \frac{1}{e ^{6}})

x = ln (x) + 1

5 = 50.238 ln (x) - 314.32

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

lo g_{2} (9 x + 2) - lo g_{2} (x - 5) = 3

ln (x + 50) = 2

What is the answer to x=ln(x)+6 ?
The answer to x=ln(x)+6 is x=-\W_{-1}(-1/(e^6)),x=-\W_{0}(-1/(e^6))
Solve for x: x=ln(x)+6
The solution is x=-\W_{-1}(-1/(e^6)),x=-\W_{0}(-1/(e^6))