What is simplify-ln(3/11) ?

The solution to simplify-ln(3/11) is -ln(3)+ln(11)

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simplify-ln(3/11)

simplify

- ln (\frac{3}{11})

- ln (3) + ln (11)

Decimal Notation

1.29928 \dots

Solution steps

- ln (\frac{3}{11})

Apply log rule:

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

ln (\frac{3}{11}) = ln (3) - ln (11)

= - (ln (3) - ln (11))

Distribute parentheses

= - (ln (3)) - (- ln (11))

Apply minus-plus rules

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

= - ln (3) + ln (11)

- lo g_{10} (4.83 x 1 0^{- 5})

e ln^{\frac{1}{x ^{2} + y ^{2}}} (x)

ln (x^{2} + x) - ln (x + 1)

3 ln (x) - 2 ln (y) + 4 ln (z)

- lo g_{10} (1.2 \cdot 1 0^{- 9})