What is 2log_{10}(p)+5log_{10}(q)-log_{10}(r) ?

The solution to 2log_{10}(p)+5log_{10}(q)-log_{10}(r) is log_{10}((p^2q^5)/r)

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simplify 2log_{10}(p)+5log_{10}(q)-log_{10}(r)

simplify

2 lo g_{10} (p) + 5 lo g_{10} (q) - lo g_{10} (r)

lo g_{10} (\frac{p ^{2} q ^{5}}{r})

Solution steps

2 lo g_{10} (p) + 5 lo g_{10} (q) - lo g_{10} (r)

2 lo g_{10} (p) = lo g_{10} (p^{2})

5 lo g_{10} (q) = lo g_{10} (q^{5})

= lo g_{10} (p^{2}) + lo g_{10} (q^{5}) - lo g_{10} (r)

Apply log rule:

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

lo g_{10} (p^{2}) + lo g_{10} (q^{5}) = lo g_{10} (p^{2} q^{5})

= lo g_{10} (p^{2} q^{5}) - lo g_{10} (r)

Apply log rule:

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

lo g_{10} (p^{2} q^{5}) - lo g_{10} (r) = lo g_{10} (\frac{p ^{2} q ^{5}}{r})

= lo g_{10} (\frac{p ^{2} q ^{5}}{r})

\frac{1}{2} lo g_{b} (x) + 5 lo g_{b} (y) - 3 lo g_{b} (x)

ln (\frac{x ^{5} \cdot ( 1 - x ) ^{45}}{A ^{5} B ^{45}})

0.22 5^{2} ln (8 \cdot 0.225)

lo g_{2} (\frac{75}{32})

10 lo g_{10} (\frac{1}{1 _{0}})

What is 2log_{10}(p)+5log_{10}(q)-log_{10}(r) ?
The solution to 2log_{10}(p)+5log_{10}(q)-log_{10}(r) is log_{10}((p^2q^5)/r)