What is 1/4 log_{10}(2x+y)-log_{10}(3x+2y) ?

The solution to 1/4 log_{10}(2x+y)-log_{10}(3x+2y) is log_{10}(((2x+y)^{1/4})/(3x+2y))

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simplify 1/4 log_{10}(2x+y)-log_{10}(3x+2y)

simplify

\frac{1}{4} lo g_{10} (2 x + y) - lo g_{10} (3 x + 2 y)

lo g_{10} (\frac{( 2 x + y ) ^{\frac{1}{4}}}{3 x + 2 y})

Solution steps

\frac{1}{4} lo g_{10} (2 x + y) - lo g_{10} (3 x + 2 y)

Apply log rule:

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

\frac{1}{4} lo g_{10} (2 x + y) = lo g_{10} ((2 x + y)^{\frac{1}{4}})

= lo g_{10} ((2 x + y)^{\frac{1}{4}}) - lo g_{10} (3 x + 2 y)

Apply log rule:

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

lo g_{10} ((2 x + y)^{\frac{1}{4}}) - lo g_{10} (3 x + 2 y) = lo g_{10} (\frac{( 2 x + y ) ^{\frac{1}{4}}}{3 x + 2 y})

= lo g_{10} (\frac{( 2 x + y ) ^{\frac{1}{4}}}{3 x + 2 y})

lo g_{9} (10) - lo g_{9} (7)

ln (\frac{e ^{9}}{12})

lo g_{10} (\frac{x ^{2} y ^{5}}{z ^{3}})

lo g_{2} (x) - lo g_{2} (x^{4})

ln (x a^{2 x} e^{x^{2}})

What is 1/4 log_{10}(2x+y)-log_{10}(3x+2y) ?
The solution to 1/4 log_{10}(2x+y)-log_{10}(3x+2y) is log_{10}(((2x+y)^{1/4})/(3x+2y))