What is expand log_{5}((a\sqrt[3]{b})/(c^4)) ?

The solution to expand log_{5}((a\sqrt[3]{b})/(c^4)) is log_{5}(a)+log_{5}(\sqrt[3]{b})-4log_{5}(c)

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expand log_{5}((a\sqrt[3]{b})/(c^4))

expand

Solution steps

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{5} (c^{4}) = 4 lo g_{5} (c)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (y) + ln (3)

2 ln (cos^{2} (t)) + 2 ln (1 + tan^{2} (t))

ln (5) + \frac{1}{2} ln (16)

5 lo g_{a} (a) - lo g_{a} (a^{4}) + lo g_{a} (a^{- 2})

lo g_{10} (100 x y)

What is expand log_{5}((a\sqrt[3]{b})/(c^4)) ?
The solution to expand log_{5}((a\sqrt[3]{b})/(c^4)) is log_{5}(a)+log_{5}(\sqrt[3]{b})-4log_{5}(c)