What is log_{10}(5x+7)-log_{10}(x) ?

The solution to log_{10}(5x+7)-log_{10}(x) is log_{10}((5x+7)/x)

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simplify log_{10}(5x+7)-log_{10}(x)

simplify

lo g_{10} (5 x + 7) - lo g_{10} (x)

lo g_{10} (\frac{5 x + 7}{x})

Solution steps

lo g_{10} (5 x + 7) - lo g_{10} (x)

Apply log rule:

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

lo g_{10} (5 x + 7) - lo g_{10} (x) = lo g_{10} (\frac{5 x + 7}{x})

= lo g_{10} (\frac{5 x + 7}{x})

ln (9) - ln (2)

lo g_{10} (\frac{n}{2})

ln ∣ 7 - 2 ∣ - \frac{3}{2} ln ∣ 2 (7) - 1 ∣ + 2 ln ∣ 7 + 3 ∣

ln (\frac{1 - 2}{2 + 1})

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

What is log_{10}(5x+7)-log_{10}(x) ?
The solution to log_{10}(5x+7)-log_{10}(x) is log_{10}((5x+7)/x)