What is expand log_{5}((p^9)/(11_{q)}) ?

The solution to expand log_{5}((p^9)/(11_{q)}) is 9log_{5}(p)-log_{5}(11)

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expand log_{5}((p^9)/(11_{q)})

expand

lo g_{5} (\frac{p ^{9}}{1 1 _{q}})

9 lo g_{5} (p) - lo g_{5} (11)

Solution steps

lo g_{5} (\frac{p ^{9}}{1 1 _{q}})

Apply log rule:

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

lo g_{5} (\frac{p ^{9}}{1 1 _{q}}) = lo g_{5} (p^{9}) - lo g_{5} (1 1_{q})

= lo g_{5} (p^{9}) - lo g_{5} (1 1_{q})

Apply log rule:

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

lo g_{5} (p^{9}) = 9 lo g_{5} (p)

= 9 lo g_{5} (p) - lo g_{5} (1 1_{q})

Apply log rule:

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

lo g_{5} (1 1_{q}) = lo g_{5} (11)

= 9 lo g_{5} (p) - lo g_{5} (11)

ln (8) + ln (10)

ln (\frac{( r + x - 1 ) !}{x ! ( r - 1 ) !} θ^{r} (1 - θ)^{x})

ln (\frac{90}{84.37})

\frac{300}{2 \cdot π \cdot 460} \cdot ln (\frac{4 + 2 \cdot 46 0 ^{2}}{25})

4.89 + lo g_{10} (\frac{0.35 - x}{0.15 - x})

What is expand log_{5}((p^9)/(11_{q)}) ?
The solution to expand log_{5}((p^9)/(11_{q)}) is 9log_{5}(p)-log_{5}(11)