What is log_{6}((2y-3)/y) ?

The solution to log_{6}((2y-3)/y) is log_{6}(2y-3)-log_{6}(y)

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simplify log_{6}((2y-3)/y)

simplify

lo g_{6} (\frac{2 y - 3}{y})

lo g_{6} (2 y - 3) - lo g_{6} (y)

Solution steps

lo g_{6} (\frac{2 y - 3}{y})

Apply log rule:

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

lo g_{6} (\frac{2 y - 3}{y}) = lo g_{6} (2 y - 3) - lo g_{6} (y)

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

lo g_{b} (5) + 3 lo g_{b} (10) - lo g_{b} (40)

lo g_{2} (x) + lo g_{2} (x + 2)

lo g_{4} (13 b^{8} c)

lo g_{9} (\frac{9}{x})

ln (x) - 8 ln (x + 5)

What is log_{6}((2y-3)/y) ?
The solution to log_{6}((2y-3)/y) is log_{6}(2y-3)-log_{6}(y)