What is the answer to log_{10}(x+ln(x))=1 ?

The answer to log_{10}(x+ln(x))=1 is x=\W_{0}(e^{10})

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log_{10}(x+ln(x))=1

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

x = W_{0} (e^{10})

Decimal Notation

x = 7.92942 \dots

Solution steps

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

Apply log rules

ln (x) = 10 - x

f (x) = g (x),

then

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

e^{l n (x)} = e^{10 - x}

Simplify

e^{l n (x)} : x

x = e^{10 - x}

Solve

x = e^{10 - x} : x = W_{0} (e^{10})

x = W_{0} (e^{10})

Verify Solutions:

x = W_{0} (e^{10})

True

The solution is

x = W_{0} (e^{10})

lo g_{5} (4 x) = 2

lo g_{x} (5) = 2

lo g_{5} (x - 6) = 1 - lo g_{5} (x - 2)

lo g_{6} (x) + lo g_{6} (x - 9) = 2

ln (x) = 2.5

What is the answer to log_{10}(x+ln(x))=1 ?
The answer to log_{10}(x+ln(x))=1 is x=\W_{0}(e^{10})
Solve for x: log_{10}(x+ln(x))=1
The solution is x=\W_{0}(e^{10})