What is log_{6}((5x^3)/y) ?

The solution to log_{6}((5x^3)/y) is log_{6}(5)+3log_{6}(x)-log_{6}(y)

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simplify log_{6}((5x^3)/y)

simplify

lo g_{6} (\frac{5 x ^{3}}{y})

lo g_{6} (5) + 3 lo g_{6} (x) - lo g_{6} (y)

Solution steps

lo g_{6} (\frac{5 x ^{3}}{y})

Apply log rule:

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

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

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

Simplify

lo g_{6} (5 x^{3}) : lo g_{6} (5) + 3 lo g_{6} (x)

= lo g_{6} (5) + 3 lo g_{6} (x) - lo g_{6} (y)

ln (\frac{4}{17})

lo g_{4} (\frac{x ^{3}}{1024 y ^{5}})

lo g_{10} (z^{8} x)

ln (\frac{e ^{5}}{8})

2 \cdot lo g_{10} (10 x)

What is log_{6}((5x^3)/y) ?
The solution to log_{6}((5x^3)/y) is log_{6}(5)+3log_{6}(x)-log_{6}(y)