What is ln(1/1-0.1)+9ln(269/9) ?

The solution to ln(1/1-0.1)+9ln(269/9) is ln(0.9)+9(ln(269)-2ln(3))

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simplify ln(1/1-0.1)+9ln(269/9)

simplify

ln (\frac{1}{1} - 0.1) + 9 ln (\frac{269}{9})

ln (0.9) + 9 (ln (269) - 2 ln (3))

Decimal Notation

30.47202 \dots

Solution steps

ln (\frac{1}{1} - 0.1) + 9 ln (\frac{269}{9})

Apply log rule:

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

ln (\frac{269}{9}) = ln (269) - ln (9)

= ln (\frac{1}{1} - 0.1) + 9 (ln (269) - ln (9))

ln (\frac{1}{1} - 0.1) = ln (0.9)

9 (ln (269) - ln (9)) = 9 (ln (269) - 2 ln (3))

= ln (0.9) + 9 (ln (269) - 2 ln (3))

- \frac{1}{4} ln (1 + 2) + \frac{1}{4} ln (1 - 2)

3 ln (\frac{3 L}{4})

5.23 + lo g_{10} (\frac{1.76 \cdot 1 0 ^{- 3}}{0.00322})

ln (\frac{25}{75})

4 ln (2) + 2 ln (x) - \frac{1}{2} ln (x + 2)

What is ln(1/1-0.1)+9ln(269/9) ?
The solution to ln(1/1-0.1)+9ln(269/9) is ln(0.9)+9(ln(269)-2ln(3))