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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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} (1 + x^{2})

lo g_{b} (\frac{a}{h})

lo g_{w} (\frac{7 x}{4})

\frac{1}{3} lo g_{10} (x) - 7 lo g_{10} (y) + 2

ln (\frac{13}{8})

lo g_{2} (\frac{8 x}{y})

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