What is simplify-1/2 ln(x)+ln(1/(sqrt(x))) ?

The solution to simplify-1/2 ln(x)+ln(1/(sqrt(x))) is -ln(x)

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simplify-1/2 ln(x)+ln(1/(sqrt(x)))

simplify

- \frac{1}{2} ln (x) + ln (\frac{1}{x})

- ln (x)

Solution steps

- \frac{1}{2} ln (x) + ln (\frac{1}{x})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} ln (x) = ln (x^{\frac{1}{2}})

= - ln (x^{\frac{1}{2}}) + ln (\frac{1}{x})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (\frac{1}{x}) - ln (x^{\frac{1}{2}}) = ln (\frac{\frac{1}{x}}{x ^{\frac{1}{2}}})

= ln (\frac{\frac{1}{x}}{x ^{\frac{1}{2}}})

Simplify

\frac{\frac{1}{x}}{x ^{\frac{1}{2}}} : \frac{1}{x}

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

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (x)

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What is simplify-1/2 ln(x)+ln(1/(sqrt(x))) ?
The solution to simplify-1/2 ln(x)+ln(1/(sqrt(x))) is -ln(x)