What is log_{10}(x)+2log_{10}(y)-3log_{10}(a) ?

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

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simplify log_{10}(x)+2log_{10}(y)-3log_{10}(a)

simplify

lo g_{10} (x) + 2 lo g_{10} (y) - 3 lo g_{10} (a)

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

Solution steps

lo g_{10} (x) + 2 lo g_{10} (y) - 3 lo g_{10} (a)

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) + lo g_{10} (y^{2}) - 3 lo g_{10} (a)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

= lo g_{10} (x y^{2}) - 3 lo g_{10} (a)

Apply log rule:

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

3 lo g_{10} (a) = lo g_{10} (a^{3})

= lo g_{10} (x y^{2}) - lo g_{10} (a^{3})

Apply log rule:

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

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

= lo g_{10} (\frac{x y ^{2}}{a ^{3}})

ln (2 x) - ln (x)

lo g_{3} (\frac{x ^{4}}{x - 4})

lo g_{10} (7) + lo g_{10} (3)

ln (x^{12} 6 - x)

lo g_{10} (7) + lo g_{10} (4)

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