What is log_{10}(x^3y^5) ?

The solution to log_{10}(x^3y^5) is 3log_{10}(x)+5log_{10}(y)

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simplify log_{10}(x^3y^5)

simplify

lo g_{10} (x^{3} y^{5})

3 lo g_{10} (x) + 5 lo g_{10} (y)

Solution steps

lo g_{10} (x^{3} y^{5})

Apply log rule:

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

lo g_{10} (x^{3} y^{5}) = lo g_{10} (x^{3}) + lo g_{10} (y^{5})

= lo g_{10} (x^{3}) + lo g_{10} (y^{5})

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

lo g_{10} (y^{5}) = 5 lo g_{10} (y)

= 3 lo g_{10} (x) + 5 lo g_{10} (y)

\frac{1}{2} (- \frac{1}{3} ln ∣ y ∣ + \frac{1}{3} ln ∣ y - 3 ∣)

lo g_{10} (10 x) + lo g_{10} (20 y) - lo g_{10} (10)

ln (\frac{23}{20})

ln (c \frac{x ^{a}}{z ^{b}})

\frac{1}{2} ln (\frac{120}{500})

What is log_{10}(x^3y^5) ?
The solution to log_{10}(x^3y^5) is 3log_{10}(x)+5log_{10}(y)