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Popular >

simplify ln(xe^{1/x})

Solution

simplify

ln (x e^{\frac{1}{x}})

Solution

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

Solution steps

ln (x e^{\frac{1}{x}})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{\frac{1}{x}}) = \frac{1}{x} ln (e)

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

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

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

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Frequently Asked Questions (FAQ)

What is ln(xe^{1/x}) ?
The solution to ln(xe^{1/x}) is ln(x)+1/x