What is log_{5}(3x+2)-log_{5}(x) ?

The solution to log_{5}(3x+2)-log_{5}(x) is log_{5}((3x+2)/x)

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simplify log_{5}(3x+2)-log_{5}(x)

simplify

lo g_{5} (3 x + 2) - lo g_{5} (x)

lo g_{5} (\frac{3 x + 2}{x})

Solution steps

lo g_{5} (3 x + 2) - lo g_{5} (x)

Apply log rule:

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

lo g_{5} (3 x + 2) - lo g_{5} (x) = lo g_{5} (\frac{3 x + 2}{x})

= lo g_{5} (\frac{3 x + 2}{x})

(lo g_{a} (x) - lo g_{a} (y)) + 8 lo g_{a} (v)

lo g_{10} (\frac{64}{z})

\frac{1}{3} lo g_{4} (x) + lo g_{4} (y) - 2

2 lo g_{10} (2 x)

ln (x yz)

What is log_{5}(3x+2)-log_{5}(x) ?
The solution to log_{5}(3x+2)-log_{5}(x) is log_{5}((3x+2)/x)