What is log_{3}((p^2)/(usqrt(w))) ?

The solution to log_{3}((p^2)/(usqrt(w))) is 2log_{3}(p)-log_{3}(u)-log_{3}(sqrt(w))

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simplify log_{3}((p^2)/(usqrt(w)))

simplify

lo g_{3} (\frac{p ^{2}}{u w})

2 lo g_{3} (p) - lo g_{3} (u) - lo g_{3} (w)

Solution steps

lo g_{3} (\frac{p ^{2}}{u w})

Apply log rule:

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

lo g_{3} (\frac{p ^{2}}{u w}) = lo g_{3} (p^{2}) - lo g_{3} (u w)

= lo g_{3} (p^{2}) - lo g_{3} (u w)

lo g_{3} (p^{2}) = 2 lo g_{3} (p)

lo g_{3} (u w) = lo g_{3} (u) + lo g_{3} (w)

= 2 lo g_{3} (p) - (lo g_{3} (u) + lo g_{3} (w))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{3} (u) + lo g_{3} (w)) = - lo g_{3} (u) - lo g_{3} (w)

= 2 lo g_{3} (p) - lo g_{3} (u) - lo g_{3} (w)

ln (\frac{a ^{- 2}}{b ^{- 4} c ^{5}})

ln (12) - ln (2)

2 lo g_{3} (u) - lo g_{3} (v)

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

2 ln (x) - 5 ln (y)

What is log_{3}((p^2)/(usqrt(w))) ?
The solution to log_{3}((p^2)/(usqrt(w))) is 2log_{3}(p)-log_{3}(u)-log_{3}(sqrt(w))