What is log_{10}(3xy^3) ?

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

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simplify log_{10}(3xy^3)

simplify

lo g_{10} (3 x y^{3})

lo g_{10} (3) + lo g_{10} (x) + 3 lo g_{10} (y)

Solution steps

lo g_{10} (3 x y^{3})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{10} (3 x y^{3}) = lo g_{10} (3) + lo g_{10} (x) + lo g_{10} (y^{3})

= lo g_{10} (3) + lo g_{10} (x) + lo g_{10} (y^{3})

Simplify

lo g_{10} (y^{3}) : 3 lo g_{10} (y)

= lo g_{10} (3) + lo g_{10} (x) + 3 lo g_{10} (y)

ln (12) + ln (3)

ln (\frac{( 3 y + 1 ) ^{4}}{y ^{2} + 1})

ln (x (x + 3))

3 (ln (10) - ln (5))

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