What is expand log_{10}((5sqrt(k))/(n^3)) ?

The solution to expand log_{10}((5sqrt(k))/(n^3)) is log_{10}(5)+log_{10}(sqrt(k))-3log_{10}(n)

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expand log_{10}((5sqrt(k))/(n^3))

expand

lo g_{10} (\frac{5 k}{n ^{3}})

lo g_{10} (5) + lo g_{10} (k) - 3 lo g_{10} (n)

Solution steps

lo g_{10} (\frac{5 k}{n ^{3}})

Apply log rule:

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

lo g_{10} (\frac{5 k}{n ^{3}}) = lo g_{10} (5 k) - lo g_{10} (n^{3})

= lo g_{10} (5 k) - lo g_{10} (n^{3})

Apply log rule:

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

lo g_{10} (n^{3}) = 3 lo g_{10} (n)

= lo g_{10} (5 k) - 3 lo g_{10} (n)

Apply log rule:

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

lo g_{10} (5 k) = lo g_{10} (5) + lo g_{10} (k)

= lo g_{10} (5) + lo g_{10} (k) - 3 lo g_{10} (n)

ln (x^{y} \cdot (1 - x)^{n - y})

\frac{1}{5} ln ∣ x - 3 ∣ - \frac{1}{5} ln ∣ x + 2 ∣

lo g_{e} (\frac{2}{3} w)

2 ln ∣ x + 2 ∣ - ln ∣ x - 4 ∣ + C

What is expand log_{10}((5sqrt(k))/(n^3)) ?
The solution to expand log_{10}((5sqrt(k))/(n^3)) is log_{10}(5)+log_{10}(sqrt(k))-3log_{10}(n)