What is simplify-ln(31/9) ?

The solution to simplify-ln(31/9) is -ln(31)+2ln(3)

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simplify-ln(31/9)

simplify

- ln (\frac{31}{9})

- ln (31) + 2 ln (3)

Decimal

- 1.23676 \dots

Solution steps

- ln (\frac{31}{9})

Apply log rule:

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

ln (\frac{31}{9}) = ln (31) - ln (9)

= - (ln (31) - ln (9))

ln (9) = 2 ln (3)

= - (ln (31) - 2 ln (3))

Distribute parentheses

= - (ln (31)) - (- 2 ln (3))

Apply minus-plus rules

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

= - ln (31) + 2 ln (3)

(ln (52) - ln (65)) (\frac{1}{3})

4 (ln (x) - 2 ln (2))

lo g_{2} (5) \cdot \frac{7}{8}

- lo g_{10} (6.4 \cdot 1 0^{- 8})

ln (\frac{- 8}{x}) + c