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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

2 lo g_{10} (y) = lo g_{10} (y^{2})

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

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

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

- lo g_{10} (7.5 \cdot 1 0^{- 6})

ln (\frac{2 e}{x})

2 ln (5) + 2 ln (x)

lo g_{10} (- 2 i)

\frac{1}{2} lo g_{3} (x) - 2 lo g_{3} (y + 8)

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