What is log_{2}((s^7)/(5t^2)) ?

The solution to log_{2}((s^7)/(5t^2)) is 7log_{2}(s)-log_{2}(5)-2log_{2}(t)

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simplify log_{2}((s^7)/(5t^2))

simplify

lo g_{2} (\frac{s ^{7}}{5 t ^{2}})

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

Solution steps

lo g_{2} (\frac{s ^{7}}{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 ^{7}}{5 t ^{2}}) = lo g_{2} (s^{7}) - lo g_{2} (5 t^{2})

= lo g_{2} (s^{7}) - lo g_{2} (5 t^{2})

lo g_{2} (s^{7}) = 7 lo g_{2} (s)

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

= 7 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)

= 7 lo g_{2} (s) - lo g_{2} (5) - 2 lo g_{2} (t)

ln (\frac{m ^{3}}{n ^{7}})

lo g_{10} (\frac{9 a ^{16}}{b ^{2}})

4 - lo g_{4} (16 y)

lo g_{10} (x^{2} + 2 x - 48) - lo g_{10} (x^{2} - 64)

- lo g_{10} (3.2 \cdot 1 0^{- 10})

What is log_{2}((s^7)/(5t^2)) ?
The solution to log_{2}((s^7)/(5t^2)) is 7log_{2}(s)-log_{2}(5)-2log_{2}(t)