What is simplify-1/3 ln(9/19) ?

The solution to simplify-1/3 ln(9/19) is -1/3 (2ln(3)-ln(19))

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simplify-1/3 ln(9/19)

simplify

- \frac{1}{3} ln (\frac{9}{19})

- \frac{1}{3} (2 ln (3) - ln (19))

Decimal Notation

0.24907 \dots

Solution steps

- \frac{1}{3} ln (\frac{9}{19})

Apply log rule:

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

ln (\frac{9}{19}) = ln (9) - ln (19)

= - \frac{1}{3} (ln (9) - ln (19))

ln (9) = 2 ln (3)

= - \frac{1}{3} (2 ln (3) - ln (19))

16.7 + 10 \cdot lo g_{10} (\frac{450}{70})

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

lo g_{10} (10) + lo g_{10} (1000)

ln (2) \frac{1}{7}

0.2871 \cdot ln (\frac{255.936}{500})

What is simplify-1/3 ln(9/19) ?
The solution to simplify-1/3 ln(9/19) is -1/3 (2ln(3)-ln(19))