What is the answer to ln(x)+x-3=0 ?

The answer to ln(x)+x-3=0 is x=\W_{0}(e^3)

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ln(x)+x-3=0

ln (x) + x - 3 = 0

x = W_{0} (e^{3})

Decimal Notation

x = 2.20794 \dots

Solution steps

ln (x) + x - 3 = 0

Move

x

to the right side

ln (x) - 3 = - x

Move

3

to the right side

ln (x) = - x + 3

f (x) = g (x),

then

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

e^{l n (x)} = e^{- x + 3}

Simplify

e^{l n (x)} : x

x = e^{- x + 3}

Solve

x = e^{- x + 3} : x = W_{0} (e^{3})

x = W_{0} (e^{3})

Verify Solutions:

x = W_{0} (e^{3})

True

The solution is

x = W_{0} (e^{3})

ln (x) = 2.7

6.2 = 1 + lo g_{10} (x)

y, x = ln (y) + 1

lo g_{x} (9) = 4

lo g_{10} (x) = 5.45