What is simplify-1/2 ln(x)+ln(x^{-1/2}) ?

The solution to simplify-1/2 ln(x)+ln(x^{-1/2}) is -ln(x)

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simplify-1/2 ln(x)+ln(x^{-1/2})

simplify

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

- ln (x)

Solution steps

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

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{- \frac{1}{2}}}{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)

ln (\frac{115}{100})

- lo g_{10} (2.4 \cdot 1 0^{- 6})

8 ln (m) + 9 ln (n)

1 + ln (\frac{∣ x ∣}{x + 1})

ln (0.84375 \cdot 0.75)

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