What is log_{10}((2x)/(x+1)) ?

The solution to log_{10}((2x)/(x+1)) is log_{10}(2)+log_{10}(x)-log_{10}(x+1)

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simplify log_{10}((2x)/(x+1))

simplify

lo g_{10} (\frac{2 x}{x + 1})

lo g_{10} (2) + lo g_{10} (x) - lo g_{10} (x + 1)

Solution steps

lo g_{10} (\frac{2 x}{x + 1})

Apply log rule:

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

lo g_{10} (\frac{2 x}{x + 1}) = lo g_{10} (2 x) - lo g_{10} (x + 1)

= lo g_{10} (2 x) - lo g_{10} (x + 1)

Simplify

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

= lo g_{10} (2) + lo g_{10} (x) - lo g_{10} (x + 1)

ln (x e^{- 7 x})

- 9 lo g_{10} (z) + 2 lo g_{10} (x) - 5 lo g_{10} (y)

ln (\frac{1}{0.8})

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

3 lo g_{6} (x) - 7 lo g_{6} (y)

What is log_{10}((2x)/(x+1)) ?
The solution to log_{10}((2x)/(x+1)) is log_{10}(2)+log_{10}(x)-log_{10}(x+1)