What is log_{10}(30000*p*q*(1-p-q)) ?

The solution to log_{10}(30000*p*q*(1-p-q)) is 4+log_{10}(3)+log_{10}(p)+log_{10}(q)+log_{10}(1-p-q)

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simplify log_{10}(30000pq*(1-p-q))

simplify

lo g_{10} (30000 \cdot p \cdot q \cdot (1 - p - q))

4 + lo g_{10} (3) + lo g_{10} (p) + lo g_{10} (q) + lo g_{10} (1 - p - q)

Solution steps

lo g_{10} (30000 pq (1 - p - q))

Factor the number:

30000 = 1 0^{4} \cdot 3

= lo g_{10} (1 0^{4} \cdot 3 pq (1 - p - q))

Apply log rule:

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

lo g_{10} (1 0^{4} \cdot 3 pq (1 - p - q)) = lo g_{10} (1 0^{4}) + lo g_{10} (3 pq (1 - p - q))

= lo g_{10} (1 0^{4}) + lo g_{10} (3 pq (1 - p - q))

Apply log rule:

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

lo g_{10} (1 0^{4}) = 4

= 4 + lo g_{10} (3 pq (1 - p - q))

Apply log rule:

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

lo g_{10} (3 pq (1 - p - q)) = lo g_{10} (3) + lo g_{10} (p) + lo g_{10} (q) + lo g_{10} (1 - p - q)

= 4 + (lo g_{10} (3) + lo g_{10} (p) + lo g_{10} (q) + lo g_{10} (1 - p - q))

Apply rule:

a + (b + c) = a + b + c

4 + (lo g_{10} (3) + lo g_{10} (p) + lo g_{10} (q) + lo g_{10} (1 - p - q)) = 4 + lo g_{10} (3) + lo g_{10} (p) + lo g_{10} (q) + lo g_{10} (1 - p - q)

= 4 + lo g_{10} (3) + lo g_{10} (p) + lo g_{10} (q) + lo g_{10} (1 - p - q)

ln (\frac{47.932}{75.29})

lo g_{10} (\frac{3 r ^{2}}{r - 8})

lo g_{b} (\frac{p ^{3} q ^{5}}{m ^{3} b ^{7}})

ln (\frac{3}{8 x ^{8} y})

ln (\frac{3700}{3000})

What is log_{10}(30000*p*q*(1-p-q)) ?
The solution to log_{10}(30000*p*q*(1-p-q)) is 4+log_{10}(3)+log_{10}(p)+log_{10}(q)+log_{10}(1-p-q)