What is expand log_{9}(x*y*z^5) ?

The solution to expand log_{9}(x*y*z^5) is log_{9}(x)+log_{9}(y)+5log_{9}(z)

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expand log_{9}(xyz^5)

expand

lo g_{9} (x \cdot y \cdot z^{5})

lo g_{9} (x) + lo g_{9} (y) + 5 lo g_{9} (z)

Solution steps

lo g_{9} (x y z^{5})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{9} (x y z^{5}) = lo g_{9} (x) + lo g_{9} (y) + lo g_{9} (z^{5})

= lo g_{9} (x) + lo g_{9} (y) + lo g_{9} (z^{5})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{9} (z^{5}) = 5 lo g_{9} (z)

= lo g_{9} (x) + lo g_{9} (y) + 5 lo g_{9} (z)

ln^{2} (\frac{10}{100})

ln (\frac{1}{θ ^{n}})

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

lo g_{10} (100 \cdot a)

\frac{1}{2} ln (\frac{17}{15})

What is expand log_{9}(x*y*z^5) ?
The solution to expand log_{9}(x*y*z^5) is log_{9}(x)+log_{9}(y)+5log_{9}(z)