What is log_{a}((a^5*\sqrt[3]{c})/(b^3)) ?

The solution to log_{a}((a^5*\sqrt[3]{c})/(b^3)) is 5+log_{a}(\sqrt[3]{c})-3log_{a}(b)

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simplify log_{a}((a^5*\sqrt[3]{c})/(b^3))

simplify

Solution steps

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{a} (b^{3}) = 3 lo g_{a} (b)

10 lo g_{10} (5.2 x 1 0^{6})

lo g_{b} (y^{4} x)

lo g_{b} (y^{4} z)

lo g_{10} (\frac{x ^{2} y ^{3}}{100})

- \frac{4}{7} \cdot lo g_{2} (\frac{4}{7}) - \frac{3}{7} \cdot lo g_{2} (\frac{3}{7})

What is log_{a}((a^5*\sqrt[3]{c})/(b^3)) ?
The solution to log_{a}((a^5*\sqrt[3]{c})/(b^3)) is 5+log_{a}(\sqrt[3]{c})-3log_{a}(b)