What is the answer to ln(x)= 1/x ?

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

Solve for x: ln(x)= 1/x

The solution is x= 1/(\W_{0)(1)}

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

x = \frac{1}{W _{0} ( 1 )}

Decimal Notation

x = 1.76322 \dots

Solution steps

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

f (x) = g (x),

then

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

e^{l n (x)} = e^{\frac{1}{x}}

Simplify

e^{l n (x)} : x

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

Solve

x = e^{\frac{1}{x}} : x = \frac{1}{W _{0} ( 1 )}

x = \frac{1}{W _{0} ( 1 )}

Verify Solutions:

x = \frac{1}{W _{0} ( 1 )}

True

The solution is

x = \frac{1}{W _{0} ( 1 )}

lo g_{2} (3 - x) = lo g_{2} (2 x + 18)

lo g_{2} (8 x - 26) + lo g_{2} (4 x - 20) = 2

3 = lo g_{10} (x) 125

lo g_{3} (x) = \frac{- 3}{2}

lo g_{25} (2 x - 1) = \frac{1}{2}