What is log_{10}(100^{4/5}x^2\sqrt[3]{y}) ?

The solution to log_{10}(100^{4/5}x^2\sqrt[3]{y}) is 8/5+2log_{10}(x)+log_{10}(\sqrt[3]{y})

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simplify log_{10}(100^{4/5}x^2\sqrt[3]{y})

simplify

Solution steps

10 0^{\frac{4}{5}} = 1 0^{\frac{8}{5}}

Apply log rule:

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

Apply log rule:

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

lo g_{10} (1 0^{\frac{8}{5}}) = \frac{8}{5}

Simplify

Apply rule:

a + (b + c) = a + b + c

4 ln (x - 4) - 2 ln (x)

lo g_{10} (2) + lo g_{10} (11) + lo g_{10} (7)

lo g_{10} (6) + lo g_{10} (2)

- lo g_{10} (2.5 \cdot 1 0^{- 4})

ln (6 x^{9}) - ln (3 x^{2})

What is log_{10}(100^{4/5}x^2\sqrt[3]{y}) ?
The solution to log_{10}(100^{4/5}x^2\sqrt[3]{y}) is 8/5+2log_{10}(x)+log_{10}(\sqrt[3]{y})