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

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

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

simplify

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

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

Solution steps

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

Simplify

x (x^{2} + 2)^{- \frac{1}{2}} : \frac{x}{( x ^{2} + 2 ) ^{\frac{1}{2}}}

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

Apply log rule:

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

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

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

Simplify

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

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

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