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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

ln (2) + 0.9 \cdot ln (2.25)

- lo g_{10} (1.6 \cdot 1 0^{- 1})

ln (\frac{1}{1 + e ^{x}})

lo g_{10} (\frac{1}{1 0 ^{3456}})

ln (\frac{3}{16})

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