What is log_{b}(x+1)-log_{b}(x) ?

The solution to log_{b}(x+1)-log_{b}(x) is log_{b}((x+1)/x)

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simplify log_{b}(x+1)-log_{b}(x)

simplify

lo g_{b} (x + 1) - lo g_{b} (x)

lo g_{b} (\frac{x + 1}{x})

Solution steps

lo g_{b} (x + 1) - lo g_{b} (x)

Apply log rule:

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

lo g_{b} (x + 1) - lo g_{b} (x) = lo g_{b} (\frac{x + 1}{x})

= lo g_{b} (\frac{x + 1}{x})

lo g_{6} (x) - lo g_{6} (x^{2})

lo g_{10} (x) + lo g_{10} (x + 5)

lo g_{10} (x) + lo g_{10} (x + 1)

ln (\frac{x}{x ^{2} + 7})

lo g_{9} (\frac{9 x ^{5}}{y})

What is log_{b}(x+1)-log_{b}(x) ?
The solution to log_{b}(x+1)-log_{b}(x) is log_{b}((x+1)/x)