What is 1/4 log_{10}(x)-1/4 log_{10}(y) ?

The solution to 1/4 log_{10}(x)-1/4 log_{10}(y) is log_{10}(\sqrt[4]{x/y})

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simplify 1/4 log_{10}(x)-1/4 log_{10}(y)

simplify

\frac{1}{4} lo g_{10} (x) - \frac{1}{4} lo g_{10} (y)

Solution steps

\frac{1}{4} lo g_{10} (x) - \frac{1}{4} lo g_{10} (y)

Apply log rule:

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

\frac{1}{4} lo g_{10} (x) = lo g_{10} (x^{\frac{1}{4}})

= lo g_{10} (x^{\frac{1}{4}}) - \frac{1}{4} lo g_{10} (y)

Apply log rule:

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

\frac{1}{4} lo g_{10} (y) = lo g_{10} (y^{\frac{1}{4}})

= lo g_{10} (x^{\frac{1}{4}}) - lo g_{10} (y^{\frac{1}{4}})

Apply log rule:

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

lo g_{10} (x^{\frac{1}{4}}) - lo g_{10} (y^{\frac{1}{4}}) = lo g_{10} (\frac{x ^{\frac{1}{4}}}{y ^{\frac{1}{4}}})

= lo g_{10} (\frac{x ^{\frac{1}{4}}}{y ^{\frac{1}{4}}})

Combine same powers :

lo g_{10} (3 x - 1) + lo g_{10} (x - 1)

lo g_{6} (\frac{( x y ) ^{6}}{z})^{4}

ln (\frac{e ^{4 x}}{x ^{2} + 1})

ln (6.56 \cdot 1 0^{- 4})

ln (6) + ln (\frac{e ^{(2.29928)}}{3})

What is 1/4 log_{10}(x)-1/4 log_{10}(y) ?
The solution to 1/4 log_{10}(x)-1/4 log_{10}(y) is log_{10}(\sqrt[4]{x/y})