What is log_{9}(4np^3) ?

The solution to log_{9}(4np^3) is log_{3}(2)+log_{9}(n)+3log_{9}(p)

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simplify log_{9}(4np^3)

simplify

lo g_{9} (4 n p^{3})

lo g_{3} (2) + lo g_{9} (n) + 3 lo g_{9} (p)

Solution steps

lo g_{9} (4 n p^{3})

Apply log rule:

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

lo g_{9} (4 n p^{3}) = lo g_{9} (4) + lo g_{9} (n) + lo g_{9} (p^{3})

= lo g_{9} (4) + lo g_{9} (n) + lo g_{9} (p^{3})

lo g_{9} (4) = lo g_{3} (2)

lo g_{9} (p^{3}) = 3 lo g_{9} (p)

= lo g_{3} (2) + lo g_{9} (n) + 3 lo g_{9} (p)

lo g_{9} (6) + \frac{1}{2} \cdot lo g_{9} (a) + \frac{1}{2} \cdot lo g_{9} (b)

\frac{1}{2} [4 ln (x + 1) + ln (x) - ln (x^{4} - 3)]

ln (\frac{6}{x ^{2} + 1})

\frac{1}{2} ln (x) - ln (9)

lo g_{x} (\frac{1}{81})

What is log_{9}(4np^3) ?
The solution to log_{9}(4np^3) is log_{3}(2)+log_{9}(n)+3log_{9}(p)