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

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

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

simplify

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

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

Solution steps

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

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

lo g_{10} (a) + 4 lo g_{10} (b)

- (\frac{3}{7}) lo g_{2} (\frac{3}{7}) - (\frac{4}{7}) lo g_{2} (\frac{4}{7})

2 ln (2) - ln (5)

ln (\frac{0.6}{0.4})

lo g_{2} (\frac{8 x ^{4}}{5})

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