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

The solution to simplify-1/2 ln(x)+ln(1/(x^2)) is -ln(x^{5/2})

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

simplify

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

- ln (x^{\frac{5}{2}})

Solution steps

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

Apply log rule:

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

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

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

Simplify

\frac{\frac{1}{x ^{2}}}{x ^{\frac{1}{2}}} : \frac{1}{x ^{\frac{5}{2}}}

= ln (\frac{1}{x ^{\frac{5}{2}}})

Apply log rule:

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

= - ln (x^{\frac{5}{2}})

ln (\frac{( \frac{0.296}{0.303} )}{9.9})

(ln (ln (3)) - ln (ln (2))) d x

2 lo g_{3^{^{'}}} (+ 4 lo g_{2^{^{'}}} (- 2 lo g_{1 2^{^{'}}} (x)))

lo g_{7} (5) + 3 lo g_{7} (x) - 6 lo g_{7} (y)

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

What is simplify-1/2 ln(x)+ln(1/(x^2)) ?
The solution to simplify-1/2 ln(x)+ln(1/(x^2)) is -ln(x^{5/2})