What is simplify-2ln(3/4)+ln(5/9) ?

The solution to simplify-2ln(3/4)+ln(5/9) is ln(80/81)

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simplify-2ln(3/4)+ln(5/9)

simplify

- 2 ln (\frac{3}{4}) + ln (\frac{5}{9})

ln (\frac{80}{81})

Decimal Notation

- 0.01242 \dots

Solution steps

- 2 ln (\frac{3}{4}) + ln (\frac{5}{9})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (\frac{3}{4}) = ln ((\frac{3}{4})^{2})

= - ln ((\frac{3}{4})^{2}) + ln (\frac{5}{9})

Apply log rule:

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

ln (\frac{5}{9}) - ln ((\frac{3}{4})^{2}) = ln (\frac{\frac{5}{9}}{( \frac{3}{4} ) ^{2}})

= ln (\frac{\frac{5}{9}}{( \frac{3}{4} ) ^{2}})

\frac{\frac{5}{9}}{( \frac{3}{4} ) ^{2}} = \frac{80}{81}

= ln (\frac{80}{81})

- lo g_{10} (7.15 x 1 0^{- 5})

3 lo g_{10} (x) - 2 lo g_{10} (x + 4)

ln (2 x + 2) - ln (x + 2)

\frac{19.15}{3219 \cdot 0.02} ln (\frac{1}{1 - 0.9})

ln (3 x) - x (\frac{1}{x})

What is simplify-2ln(3/4)+ln(5/9) ?
The solution to simplify-2ln(3/4)+ln(5/9) is ln(80/81)