What is log_{10}(3H)-2log_{10}(3S)+5log_{10}(3B) ?

The solution to log_{10}(3H)-2log_{10}(3S)+5log_{10}(3B) is log_{10}((81HB^5)/(S^2))

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simplify log_{10}(3H)-2log_{10}(3S)+5log_{10}(3B)

simplify

lo g_{10} (3 H) - 2 lo g_{10} (3 S) + 5 lo g_{10} (3 B)

lo g_{10} (\frac{81 H B ^{5}}{S ^{2}})

Solution steps

lo g_{10} (3 H) - 2 lo g_{10} (3 S) + 5 lo g_{10} (3 B)

- 2 lo g_{10} (3 S) = - lo g_{10} ((3 S)^{2})

5 lo g_{10} (3 B) = lo g_{10} ((3 B)^{5})

= lo g_{10} (3 H) - lo g_{10} ((3 S)^{2}) + lo g_{10} ((3 B)^{5})

Apply log rule:

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

lo g_{10} (3 H) - lo g_{10} ((3 S)^{2}) = lo g_{10} (\frac{3 H}{( 3 S ) ^{2}})

= lo g_{10} (\frac{3 H}{( 3 S ) ^{2}}) + lo g_{10} ((3 B)^{5})

Apply log rule:

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

lo g_{10} (\frac{3 H}{( 3 S ) ^{2}}) + lo g_{10} ((3 B)^{5}) = lo g_{10} (\frac{3 H}{( 3 S ) ^{2}} (3 B)^{5})

= lo g_{10} (\frac{3 H}{( 3 S ) ^{2}} (3 B)^{5})

Simplify

\frac{3 H}{( 3 S ) ^{2}} (3 B)^{5} : \frac{81 H B ^{5}}{S ^{2}}

= lo g_{10} (\frac{81 H B ^{5}}{S ^{2}})

lo g_{3} (5 x y)

2 lo g_{y} (- 3 lo g_{x} (- 2 lo g_{10} (x)))

lo g_{2} (\frac{5 y}{7})

lo g_{10} (6) 6

lo g_{3} (\frac{x ^{14}}{x - 2})

What is log_{10}(3H)-2log_{10}(3S)+5log_{10}(3B) ?
The solution to log_{10}(3H)-2log_{10}(3S)+5log_{10}(3B) is log_{10}((81HB^5)/(S^2))