What is log_{2}((s^9)/(5t^2)) ?

The solution to log_{2}((s^9)/(5t^2)) is 9log_{2}(s)-log_{2}(5)-2log_{2}(t)

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simplify log_{2}((s^9)/(5t^2))

simplify

lo g_{2} (\frac{s ^{9}}{5 t ^{2}})

9 lo g_{2} (s) - lo g_{2} (5) - 2 lo g_{2} (t)

Solution steps

lo g_{2} (\frac{s ^{9}}{5 t ^{2}})

Apply log rule:

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

lo g_{2} (\frac{s ^{9}}{5 t ^{2}}) = lo g_{2} (s^{9}) - lo g_{2} (5 t^{2})

= lo g_{2} (s^{9}) - lo g_{2} (5 t^{2})

lo g_{2} (s^{9}) = 9 lo g_{2} (s)

lo g_{2} (5 t^{2}) = lo g_{2} (5) + 2 lo g_{2} (t)

= 9 lo g_{2} (s) - (lo g_{2} (5) + 2 lo g_{2} (t))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{2} (5) + 2 lo g_{2} (t)) = - lo g_{2} (5) - 2 lo g_{2} (t)

= 9 lo g_{2} (s) - lo g_{2} (5) - 2 lo g_{2} (t)

lo g_{4} (y - 1) + lo g_{4} (\frac{x}{2})

ln (\frac{2 x + 1}{1 - x})

ln (\frac{2 x}{x})

lo g_{5} (\frac{125}{x + 6})

lo g_{10} (\frac{x + y}{10})

What is log_{2}((s^9)/(5t^2)) ?
The solution to log_{2}((s^9)/(5t^2)) is 9log_{2}(s)-log_{2}(5)-2log_{2}(t)