What is the answer to x=-log_{10}(x) ?

The answer to x=-log_{10}(x) is x=(\W_{0}(ln(10)))/(ln(10))

Solve for x: x=-log_{10}(x)

The solution is x=(\W_{0}(ln(10)))/(ln(10))

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x = - lo g_{10} (x)

x = \frac{W _{0} ( ln ( 10 ) )}{ln ( 10 )}

Decimal Notation

x = 0.39901 \dots

Solution steps

x = - lo g_{10} (x)

Move

lo g_{10} (x)

to the left side

x + lo g_{10} (x) = 0

Move

x

to the right side

lo g_{10} (x) = - x

f (x) = g (x),

then

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

1 0^{l o g_{10} (x)} = 1 0^{- x}

Simplify

1 0^{l o g_{10} (x)} : x

x = 1 0^{- x}

Solve

x = 1 0^{- x} : x = \frac{W _{0} ( ln ( 10 ) )}{ln ( 10 )}

x = \frac{W _{0} ( ln ( 10 ) )}{ln ( 10 )}

Verify Solutions:

x = \frac{W _{0} ( ln ( 10 ) )}{ln ( 10 )}

True

The solution is

x = \frac{W _{0} ( ln ( 10 ) )}{ln ( 10 )}

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

ln (3 x^{2} + 2 x) = 0

lo g_{3} (7 x - 1) = 3

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

12 lo g_{x} (5) + lo g_{5} (x) - 7 = 0

What is the answer to x=-log_{10}(x) ?
The answer to x=-log_{10}(x) is x=(\W_{0}(ln(10)))/(ln(10))
Solve for x: x=-log_{10}(x)
The solution is x=(\W_{0}(ln(10)))/(ln(10))