What is log_{6}(5z^{-3}) ?

The solution to log_{6}(5z^{-3}) is log_{6}(5)-3log_{6}(z)

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simplify log_{6}(5z^{-3})

simplify

lo g_{6} (5 z^{- 3})

lo g_{6} (5) - 3 lo g_{6} (z)

Solution steps

lo g_{6} (5 z^{- 3})

Simplify

5 z^{- 3} : \frac{5}{z ^{3}}

= lo g_{6} (\frac{5}{z ^{3}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{6} (\frac{5}{z ^{3}}) = lo g_{6} (5) - lo g_{6} (z^{3})

= lo g_{6} (5) - lo g_{6} (z^{3})

Simplify

lo g_{6} (z^{3}) : 3 lo g_{6} (z)

= lo g_{6} (5) - 3 lo g_{6} (z)

lo g_{b} (x) + lo g_{b} (y) - lo g_{b} (z)

lo g_{x} (\frac{2}{3})

lo g_{10} (\frac{\frac{1}{9}}{k})

ln (x y) + 9 ln (\frac{y}{z}) - 8 ln (x yz)

5 lo g_{10} (y) - 3 lo g_{10} (m)

What is log_{6}(5z^{-3}) ?
The solution to log_{6}(5z^{-3}) is log_{6}(5)-3log_{6}(z)