What is simplify-ln(33/9) ?

The solution to simplify-ln(33/9) is -ln(33)+2ln(3)

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simplify-ln(33/9)

simplify

- ln (\frac{33}{9})

- ln (33) + 2 ln (3)

Decimal Notation

- 1.29928 \dots

Solution steps

- ln (\frac{33}{9})

Apply log rule:

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

ln (\frac{33}{9}) = ln (33) - ln (9)

= - (ln (33) - ln (9))

ln (9) = 2 ln (3)

= - (ln (33) - 2 ln (3))

Distribute parentheses

= - (ln (33)) - (- 2 ln (3))

Apply minus-plus rules

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

= - ln (33) + 2 ln (3)

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