What is simplify-1/5 ln(-1)-1/5 ln(3) ?

The solution to simplify-1/5 ln(-1)-1/5 ln(3) is -ln(-3^{1/5})

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simplify-1/5 ln(-1)-1/5 ln(3)

simplify

- \frac{1}{5} ln (- 1) - \frac{1}{5} ln (3)

- ln (- 3^{\frac{1}{5}})

Decimal Notation

- 0.21972 \dots

Solution steps

- \frac{1}{5} ln (- 1) - \frac{1}{5} ln (3)

Apply log rule:

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

\frac{1}{5} ln (- 1) = ln ((- 1)^{\frac{1}{5}})

= - ln ((- 1)^{\frac{1}{5}}) - \frac{1}{5} ln (3)

Apply log rule:

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

\frac{1}{5} ln (3) = ln (3^{\frac{1}{5}})

= - ln ((- 1)^{\frac{1}{5}}) - ln (3^{\frac{1}{5}})

Rewrite

- ln ((- 1)^{\frac{1}{5}}) - ln (3^{\frac{1}{5}})

- (ln ((- 1)^{\frac{1}{5}}) + ln (3^{\frac{1}{5}}))

= - (ln (3^{\frac{1}{5}}) + ln ((- 1)^{\frac{1}{5}}))

Apply log rule:

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

ln ((- 1)^{\frac{1}{5}}) + ln (3^{\frac{1}{5}}) = ln ((- 1)^{\frac{1}{5}} \cdot 3^{\frac{1}{5}})

= - ln ((- 1)^{\frac{1}{5}} \cdot 3^{\frac{1}{5}})

(- 1)^{\frac{1}{5}} \cdot 3^{\frac{1}{5}} = - 3^{\frac{1}{5}}

= - ln (- 3^{\frac{1}{5}})

(\frac{1}{6}) \cdot ln (\frac{11.92}{8.2})

4.74472 + lo g_{10} (\frac{0.10774}{0.06322})

ln (\frac{6.2}{1.5})

ln (4 x e^{- x^{2}})

1000 \cdot ln (\frac{373}{273})

What is simplify-1/5 ln(-1)-1/5 ln(3) ?
The solution to simplify-1/5 ln(-1)-1/5 ln(3) is -ln(-3^{1/5})