What is the answer to 1/x =(ln(x)+x)/x ?

The answer to 1/x =(ln(x)+x)/x is x=1

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1/x =(ln(x)+x)/x

\frac{1}{x} = \frac{ln ( x ) + x}{x}

x = 1

Solution steps

\frac{1}{x} = \frac{ln ( x ) + x}{x}

Switch sides

\frac{ln ( x ) + x}{x} = \frac{1}{x}

Multiply both sides by

x

ln (x) + x = 1

Move

x

to the right side

ln (x) = 1 - x

f (x) = g (x),

then

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

e^{l n (x)} = e^{1 - x}

Simplify

e^{l n (x)} : x

x = e^{1 - x}

Solve

x = e^{1 - x} : x = 1

x = 1

Verify Solutions:

x = 1

True

The solution is

x = 1

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

9.1 = 10 lo g_{10} (\frac{4.8}{x})

t, lo g_{5} (t) = u

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

ln (3 x - 16) = 7