What is log_{6}(xy^3z^{-2}) ?

The solution to log_{6}(xy^3z^{-2}) is log_{6}(x)+3log_{6}(y)-2log_{6}(z)

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simplify log_{6}(xy^3z^{-2})

simplify

lo g_{6} (x y^{3} z^{- 2})

lo g_{6} (x) + 3 lo g_{6} (y) - 2 lo g_{6} (z)

Solution steps

lo g_{6} (x y^{3} z^{- 2})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{6} (x y^{3} z^{- 2}) = lo g_{6} (x) + lo g_{6} (y^{3}) + lo g_{6} (z^{- 2})

= lo g_{6} (x) + lo g_{6} (y^{3}) + lo g_{6} (z^{- 2})

lo g_{6} (y^{3}) = 3 lo g_{6} (y)

lo g_{6} (z^{- 2}) = - 2 lo g_{6} (z)

= lo g_{6} (x) + 3 lo g_{6} (y) - 2 lo g_{6} (z)

lo g_{3} (\frac{27}{x + 7})

ln (l + x^{2} + y^{2}) - ln (x)

- 4 (ln ∣ 2 a - 10 ∣ - ln (10))

lo g_{3} (\frac{81}{x - 9})

- ln ∣ x - 2 ∣ + ln ∣ x - 3 ∣ + C

What is log_{6}(xy^3z^{-2}) ?
The solution to log_{6}(xy^3z^{-2}) is log_{6}(x)+3log_{6}(y)-2log_{6}(z)