What is log_{10}(3x+1)-log_{10}(x) ?

The solution to log_{10}(3x+1)-log_{10}(x) is log_{10}((3x+1)/x)

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simplify log_{10}(3x+1)-log_{10}(x)

simplify

lo g_{10} (3 x + 1) - lo g_{10} (x)

lo g_{10} (\frac{3 x + 1}{x})

Solution steps

lo g_{10} (3 x + 1) - 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 + 1) - lo g_{10} (x) = lo g_{10} (\frac{3 x + 1}{x})

= lo g_{10} (\frac{3 x + 1}{x})

lo g_{3} (x^{2} y^{3})

\frac{1}{3} lo g_{b} (x) - lo g_{b} (y)

ln (\frac{2}{3 x ^{3} y})

2 ln (x) - \frac{1}{3} ln (x) + 3 ln (x - 1) + 3 ln (x^{2} - 2 x + 1)

lo g_{4} (\frac{y}{64})

What is log_{10}(3x+1)-log_{10}(x) ?
The solution to log_{10}(3x+1)-log_{10}(x) is log_{10}((3x+1)/x)