What is the answer to 2log_{10}(x)-log_{10}(3)+x=0 ?

The answer to 2log_{10}(x)-log_{10}(3)+x=0 is x=(2\W_{0}((ln(10)e^{\frac{ln(3))/2})/(2))}{ln(10)}

Solve for x: 2log_{10}(x)-log_{10}(3)+x=0

The solution is x=(2\W_{0}((ln(10)e^{\frac{ln(3))/2})/(2))}{ln(10)}

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2 lo g_{10} (x) - lo g_{10} (3) + x = 0

x = \frac{2 W _{0} ( \frac{l n ( 10 ) e ^{\frac{l n ( 3 )}{2}}}{2} )}{ln ( 10 )}

Decimal Notation

x = 0.73938 \dots

Solution steps

2 lo g_{10} (x) - lo g_{10} (3) + x = 0

Move

lo g_{10} (3)

to the right side

2 lo g_{10} (x) + x = lo g_{10} (3)

Move

x

to the right side

2 lo g_{10} (x) = lo g_{10} (3) - x

Divide both sides by

2

lo g_{10} (x) = \frac{lo g _{10} ( 3 ) - x}{2}

f (x) = g (x),

then

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

1 0^{l o g_{10} (x)} = 1 0^{\frac{l o g _{10} ( 3 ) - x}{2}}

Simplify

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

x = 1 0^{\frac{l o g _{10} ( 3 ) - x}{2}}

Solve

x = 1 0^{\frac{l o g _{10} ( 3 ) - x}{2}} : x = \frac{2 W _{0} ( \frac{l n ( 10 ) e ^{\frac{l n ( 3 )}{2}}}{2} )}{ln ( 10 )}

x = \frac{2 W _{0} ( \frac{l n ( 10 ) e ^{\frac{l n ( 3 )}{2}}}{2} )}{ln ( 10 )}

Verify Solutions:

x = \frac{2 W _{0} ( \frac{l n ( 10 ) e ^{\frac{l n ( 3 )}{2}}}{2} )}{ln ( 10 )}

True

The solution is

x = \frac{2 W _{0} ( \frac{l n ( 10 ) e ^{\frac{l n ( 3 )}{2}}}{2} )}{ln ( 10 )}

1 + lo g_{5} (x^{2} + 1) = lo g_{5} (x^{2} + 4 x + 1)

x, 2 lo g_{4} (x) - lo g_{2} (y) = 3

ln (2 x - 2) = 0

ln (2 x - 2) = 2

lo g_{2} (x) + lo g_{2} (x^{2}) + lo g_{3} (x^{3}) = 6

What is the answer to 2log_{10}(x)-log_{10}(3)+x=0 ?
The answer to 2log_{10}(x)-log_{10}(3)+x=0 is x=(2\W_{0}((ln(10)e^{\frac{ln(3))/2})/(2))}{ln(10)}
Solve for x: 2log_{10}(x)-log_{10}(3)+x=0
The solution is x=(2\W_{0}((ln(10)e^{\frac{ln(3))/2})/(2))}{ln(10)}