What is log_{9}((u^2)/(s^3t^4)) ?

The solution to log_{9}((u^2)/(s^3t^4)) is log_{3}(u)-3log_{9}(s)-4log_{9}(t)

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simplify log_{9}((u^2)/(s^3t^4))

simplify

lo g_{9} (\frac{u ^{2}}{s ^{3} t ^{4}})

lo g_{3} (u) - 3 lo g_{9} (s) - 4 lo g_{9} (t)

Solution steps

lo g_{9} (\frac{u ^{2}}{s ^{3} t ^{4}})

Apply log rule:

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

lo g_{9} (\frac{u ^{2}}{s ^{3} t ^{4}}) = lo g_{9} (u^{2}) - lo g_{9} (s^{3} t^{4})

= lo g_{9} (u^{2}) - lo g_{9} (s^{3} t^{4})

lo g_{9} (u^{2}) = lo g_{3} (u)

lo g_{9} (s^{3} t^{4}) = 3 lo g_{9} (s) + 4 lo g_{9} (t)

= lo g_{3} (u) - (3 lo g_{9} (s) + 4 lo g_{9} (t))

Apply the distributive law:

- (a + b) = - a - b

- (3 lo g_{9} (s) + 4 lo g_{9} (t)) = - 3 lo g_{9} (s) - 4 lo g_{9} (t)

= lo g_{3} (u) - 3 lo g_{9} (s) - 4 lo g_{9} (t)

lo g_{b} (x) + lo g_{b} (x + 2) - lo g_{b} (8)

lo g_{5} (\frac{x ^{2}}{y ^{2} z ^{3}})

- lo g_{10} (3.5 \cdot 1 0^{- 5})

lo g_{10} (c) - 2 lo g_{10} (g)

lo g_{4} (7 x)

What is log_{9}((u^2)/(s^3t^4)) ?
The solution to log_{9}((u^2)/(s^3t^4)) is log_{3}(u)-3log_{9}(s)-4log_{9}(t)