What is simplify-ln(5/9) ?

The solution to simplify-ln(5/9) is -ln(5)+2ln(3)

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simplify-ln(5/9)

simplify

- ln (\frac{5}{9})

- ln (5) + 2 ln (3)

Decimal Notation

0.58778 \dots

Solution steps

- ln (\frac{5}{9})

Apply log rule:

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

ln (\frac{5}{9}) = ln (5) - ln (9)

= - (ln (5) - ln (9))

ln (9) = 2 ln (3)

= - (ln (5) - 2 ln (3))

Distribute parentheses

= - (ln (5)) - (- 2 ln (3))

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - ln (5) + 2 ln (3)

ln (\frac{14}{5})

\frac{1}{5} lo g_{10} (5)

ln (\frac{53}{55})

lo g_{3} (6) - lo g_{3} (13)

3 ln (\frac{3}{13})