What is log_{10}(3x+2)-log_{10}(x) ?

The solution to log_{10}(3x+2)-log_{10}(x) is log_{10}((3x+2)/x)

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simplify log_{10}(3x+2)-log_{10}(x)

simplify

lo g_{10} (3 x + 2) - lo g_{10} (x)

lo g_{10} (\frac{3 x + 2}{x})

Solution steps

lo g_{10} (3 x + 2) - lo g_{10} (x)

Apply log rule:

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

lo g_{10} (3 x + 2) - lo g_{10} (x) = lo g_{10} (\frac{3 x + 2}{x})

= lo g_{10} (\frac{3 x + 2}{x})

2 ln (\frac{3}{2}) - ln (4)

lo g_{10} (\frac{1}{x ^{2}})

lo g_{9} (x y)

ln (\frac{1}{1000})

ln^{2} (\frac{1}{2})

What is log_{10}(3x+2)-log_{10}(x) ?
The solution to log_{10}(3x+2)-log_{10}(x) is log_{10}((3x+2)/x)