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Popular >

simplify 1/3 ln(6)-1/3 ln(-1)

Solution

simplify

\frac{1}{3} ln (6) - \frac{1}{3} ln (- 1)

Solution

ln (- 6^{\frac{1}{3}})

+1

Decimal Notation

0.59725 \dots

Solution steps

\frac{1}{3} ln (6) - \frac{1}{3} ln (- 1)

Apply log rule:

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

\frac{1}{3} ln (6) = ln (6^{\frac{1}{3}})

= ln (6^{\frac{1}{3}}) - \frac{1}{3} ln (- 1)

Apply log rule:

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

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

= ln (6^{\frac{1}{3}}) - ln ((- 1)^{\frac{1}{3}})

Apply log rule:

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

ln (6^{\frac{1}{3}}) - ln ((- 1)^{\frac{1}{3}}) = ln (\frac{6 ^{\frac{1}{3}}}{( - 1 ) ^{\frac{1}{3}}})

= ln (\frac{6 ^{\frac{1}{3}}}{( - 1 ) ^{\frac{1}{3}}})

\frac{6 ^{\frac{1}{3}}}{( - 1 ) ^{\frac{1}{3}}} = - 6^{\frac{1}{3}}

= ln (- 6^{\frac{1}{3}})

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Frequently Asked Questions (FAQ)

What is 1/3 ln(6)-1/3 ln(-1) ?
The solution to 1/3 ln(6)-1/3 ln(-1) is ln(-6^{1/3})