What is log_{5}((3y-8)/y) ?

The solution to log_{5}((3y-8)/y) is log_{5}(3y-8)-log_{5}(y)

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simplify log_{5}((3y-8)/y)

simplify

lo g_{5} (\frac{3 y - 8}{y})

lo g_{5} (3 y - 8) - lo g_{5} (y)

Solution steps

lo g_{5} (\frac{3 y - 8}{y})

Apply log rule:

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

lo g_{5} (\frac{3 y - 8}{y}) = lo g_{5} (3 y - 8) - lo g_{5} (y)

= lo g_{5} (3 y - 8) - lo g_{5} (y)

ln (\frac{x x - 4}{x ^{5} + 7})

3 ln (x) + 5 ln (y)

lo g_{10} (\frac{6 z}{10})

lo g_{b} (\frac{x y}{z})

ln (3) + 4 ln (2)

What is log_{5}((3y-8)/y) ?
The solution to log_{5}((3y-8)/y) is log_{5}(3y-8)-log_{5}(y)