What is log_{10}((9x^4y)/(\sqrt[5]{y)}) ?

The solution to log_{10}((9x^4y)/(\sqrt[5]{y)}) is 2log_{10}(3)+4log_{10}(x)+4/5 log_{10}(y)

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simplify log_{10}((9x^4y)/(\sqrt[5]{y)})

simplify

2 lo g_{10} (3) + 4 lo g_{10} (x) + \frac{4}{5} lo g_{10} (y)

Solution steps

Cancel

= lo g_{10} (9 x^{4} y^{\frac{4}{5}})

Apply log rule:

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

lo g_{10} (9 x^{4} y^{\frac{4}{5}}) = lo g_{10} (9) + lo g_{10} (x^{4}) + lo g_{10} (y^{\frac{4}{5}})

= lo g_{10} (9) + lo g_{10} (x^{4}) + lo g_{10} (y^{\frac{4}{5}})

lo g_{10} (9) = 2 lo g_{10} (3)

lo g_{10} (x^{4}) = 4 lo g_{10} (x)

lo g_{10} (y^{\frac{4}{5}}) = \frac{4}{5} lo g_{10} (y)

= 2 lo g_{10} (3) + 4 lo g_{10} (x) + \frac{4}{5} lo g_{10} (y)

- lo g_{10} (7.2 \cdot 1 0^{- 4})

lo g_{10} (5 x^{2} y)

ln (4) + ln (5)

lo g_{3} (\frac{27}{x + 5})

\frac{2}{5} lo g_{2} (\frac{2}{5}) + \frac{3}{5} lo g_{2} (\frac{3}{5})

What is log_{10}((9x^4y)/(\sqrt[5]{y)}) ?
The solution to log_{10}((9x^4y)/(\sqrt[5]{y)}) is 2log_{10}(3)+4log_{10}(x)+4/5 log_{10}(y)