What is the answer to 0.001=(ln(x))/x ?

The answer to 0.001=(ln(x))/x is x=-(\W_{-1}(-1/1000))/(0.001),x=-(\W_{0}(-1/1000))/(0.001)

Solve for x: 0.001=(ln(x))/x

The solution is x=-(\W_{-1}(-1/1000))/(0.001),x=-(\W_{0}(-1/1000))/(0.001)

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0.001 = \frac{ln ( x )}{x}

x = - \frac{W _{- 1} ( - \frac{1}{1000} )}{0.001}, x = - \frac{W _{0} ( - \frac{1}{1000} )}{0.001}

Decimal

x = 9118.00647 \dots, x = 1.00100 \dots

Solution steps

0.001 = \frac{ln ( x )}{x}

Switch sides

\frac{ln ( x )}{x} = 0.001

Multiply both sides by

x

ln (x) = 0.001 x

f (x) = g (x),

then

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

e^{l n (x)} = e^{0.001 x}

Simplify

e^{l n (x)} : x

x = e^{0.001 x}

Solve

x = e^{0.001 x} : x = - \frac{W _{- 1} ( - \frac{1}{1000} )}{0.001}, x = - \frac{W _{0} ( - \frac{1}{1000} )}{0.001}

x = - \frac{W _{- 1} ( - \frac{1}{1000} )}{0.001}, x = - \frac{W _{0} ( - \frac{1}{1000} )}{0.001}

Verify Solutions:

x = - \frac{W _{- 1} ( - \frac{1}{1000} )}{0.001}

True

, x = - \frac{W _{0} ( - \frac{1}{1000} )}{0.001}

True

The solutions are

x = - \frac{W _{- 1} ( - \frac{1}{1000} )}{0.001}, x = - \frac{W _{0} ( - \frac{1}{1000} )}{0.001}

20 x^{3} ln (x) + 9 x^{3} = 0

ln (x) = \frac{1}{3}

56 x^{6} ln (x) + 15 x^{6} = 0

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

20 ln (0.05 \times x - 1) + 0.83 = 7

What is the answer to 0.001=(ln(x))/x ?
The answer to 0.001=(ln(x))/x is x=-(\W_{-1}(-1/1000))/(0.001),x=-(\W_{0}(-1/1000))/(0.001)
Solve for x: 0.001=(ln(x))/x
The solution is x=-(\W_{-1}(-1/1000))/(0.001),x=-(\W_{0}(-1/1000))/(0.001)