What is log_{3}(z\sqrt[3]{x*y}) ?

The solution to log_{3}(z\sqrt[3]{x*y}) is log_{3}(z)+log_{3}(\sqrt[3]{xy})

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simplify log_{3}(z\sqrt[3]{x*y})

simplify

Solution steps

Apply log rule:

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

- lo g_{10} (2 \times 1 0^{- 5})

2 lo g_{6} (5 a) + lo g_{6} (b) + 7 lo g_{6} (c)

ln (- 1) + ln (- 3)

ln (8) + ln (4)

lo g_{\frac{1}{2}} (8 x)

What is log_{3}(z\sqrt[3]{x*y}) ?
The solution to log_{3}(z\sqrt[3]{x*y}) is log_{3}(z)+log_{3}(\sqrt[3]{xy})