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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (2) + lo g_{10} (x) = lo g_{10} (2 x)

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

Apply log rule:

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

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

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

ln (x + 2) + ln (x - 2)

ln (3) + \frac{1}{3} ln (8)

3 lo g_{12} (2) + \frac{1}{3} lo g_{12} (8) - lo g_{12} (4)

- lo g_{10} (1.3 \times 1 0^{- 4})

ln (\frac{1}{130})

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