What is simplify-1/3 ln((5+1)/(5-2)) ?

The solution to simplify-1/3 ln((5+1)/(5-2)) is -(ln(6)-ln(3))/3

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simplify-1/3 ln((5+1)/(5-2))

simplify

- \frac{1}{3} ln (\frac{5 + 1}{5 - 2})

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

Decimal Notation

- 0.23104 \dots

Solution steps

- \frac{1}{3} ln (\frac{5 + 1}{5 - 2})

Apply log rule:

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

ln (\frac{5 + 1}{5 - 2}) = ln (5 + 1) - ln (5 - 2)

= - \frac{1}{3} (ln (5 + 1) - ln (5 - 2))

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{1 \cdot ( ln ( 5 + 1 ) - ln ( 5 - 2 ) )}{3}

1 \cdot (ln (5 + 1) - ln (5 - 2)) = ln (6) - ln (3)

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

ln (\frac{x ^{3}}{y ^{2}})

lo g_{0.5} (x^{2})

4 ln (\frac{97}{100})

\frac{1}{2} \cdot \frac{ln ( 0.5 ) - ln ( z )}{\frac{z}{2} \cdot ( ln ( 2 ) ) ^{2}}

lo g_{e} (- \frac{1}{6} (x^{2} - 6 x + 5))

What is simplify-1/3 ln((5+1)/(5-2)) ?
The solution to simplify-1/3 ln((5+1)/(5-2)) is -(ln(6)-ln(3))/3