What is expand log_{6}(x*y*z^5) ?

The solution to expand log_{6}(x*y*z^5) is log_{6}(x)+log_{6}(y)+5log_{6}(z)

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expand log_{6}(xyz^5)

expand

lo g_{6} (x \cdot y \cdot z^{5})

lo g_{6} (x) + lo g_{6} (y) + 5 lo g_{6} (z)

Solution steps

lo g_{6} (x y z^{5})

Apply log rule:

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

lo g_{6} (x y z^{5}) = lo g_{6} (x) + lo g_{6} (y) + lo g_{6} (z^{5})

= lo g_{6} (x) + lo g_{6} (y) + lo g_{6} (z^{5})

Apply log rule:

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

lo g_{6} (z^{5}) = 5 lo g_{6} (z)

= lo g_{6} (x) + lo g_{6} (y) + 5 lo g_{6} (z)

ln (\frac{x + 6}{e ^{x}})

lo g_{12} (+ \frac{1}{2} lo g_{7} (- lo g_{2} (x)))

lo g_{3} (x^{7} 3 y^{6})

lo g_{10} (8 (1 + 3 x))

lo g_{10} (\frac{m}{10 n})

What is expand log_{6}(x*y*z^5) ?
The solution to expand log_{6}(x*y*z^5) is log_{6}(x)+log_{6}(y)+5log_{6}(z)