What is log_{3}((\sqrt[3]{3}0.27)/(81)) ?

The solution to log_{3}((\sqrt[3]{3}0.27)/(81)) is log_{3}(0.27)-11/3

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simplify log_{3}((\sqrt[3]{3}0.27)/(81))

simplify

lo g_{3} (0.27) - \frac{11}{3}

Decimal Notation

- 4.85847 \dots

Solution steps

Apply log rule:

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

= \frac{1}{3} + lo g_{3} (0.27) - lo g_{3} (81)

lo g_{3} (81) = 4

= \frac{1}{3} + lo g_{3} (0.27) - 4

Combine the fractions

- 4 + \frac{1}{3} : - \frac{11}{3}

= lo g_{3} (0.27) - \frac{11}{3}

3 ln (x) - 5 ln (y) - \frac{1}{4} ln (x)

lo g_{3} (\frac{x + 33 x}{( x - 1 ) ( x - 5 )})

lo g_{2} (\frac{1}{2} x^{2} y)

ln (\frac{e ^{3} 2}{e ^{\frac{1}{3}}}) - e^{2 l n (2)}

- ln (a) - ln (b)

What is log_{3}((\sqrt[3]{3}0.27)/(81)) ?
The solution to log_{3}((\sqrt[3]{3}0.27)/(81)) is log_{3}(0.27)-11/3