What is the answer to x+log_{3}(x)=0 ?

The answer to x+log_{3}(x)=0 is x=(\W_{0}(ln(3)))/(ln(3))

Solve for x: x+log_{3}(x)=0

The solution is x=(\W_{0}(ln(3)))/(ln(3))

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x + lo g_{3} (x) = 0

x = \frac{W _{0} ( ln ( 3 ) )}{ln ( 3 )}

Decimal Notation

x = 0.54780 \dots

Solution steps

x + lo g_{3} (x) = 0

Move

x

to the right side

lo g_{3} (x) = - x

f (x) = g (x),

then

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

3^{l o g_{3} (x)} = 3^{- x}

Simplify

3^{l o g_{3} (x)} : x

x = 3^{- x}

Solve

x = 3^{- x} : x = \frac{W _{0} ( ln ( 3 ) )}{ln ( 3 )}

x = \frac{W _{0} ( ln ( 3 ) )}{ln ( 3 )}

Verify Solutions:

x = \frac{W _{0} ( ln ( 3 ) )}{ln ( 3 )}

True

The solution is

x = \frac{W _{0} ( ln ( 3 ) )}{ln ( 3 )}

lo g_{2} (25 - x) = - 3

20 \cdot lo g_{10} (y) = 12

lo g_{4} (x^{2} - 6 x) = 2

lo g_{10} (x) = 3.2

ln (x + 2) + ln (x - 2) = ln (12)

What is the answer to x+log_{3}(x)=0 ?
The answer to x+log_{3}(x)=0 is x=(\W_{0}(ln(3)))/(ln(3))
Solve for x: x+log_{3}(x)=0
The solution is x=(\W_{0}(ln(3)))/(ln(3))