What is expand log_{b}((x^2y)/(z^4)) ?

The solution to expand log_{b}((x^2y)/(z^4)) is 2log_{b}(x)+log_{b}(y)-4log_{b}(z)

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expand log_{b}((x^2y)/(z^4))

expand

lo g_{b} (\frac{x ^{2} y}{z ^{4}})

2 lo g_{b} (x) + lo g_{b} (y) - 4 lo g_{b} (z)

Solution steps

lo g_{b} (\frac{x ^{2} y}{z ^{4}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{b} (\frac{x ^{2} y}{z ^{4}}) = lo g_{b} (x^{2} y) - lo g_{b} (z^{4})

= lo g_{b} (x^{2} y) - lo g_{b} (z^{4})

Apply log rule:

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

lo g_{b} (z^{4}) = 4 lo g_{b} (z)

= lo g_{b} (x^{2} y) - 4 lo g_{b} (z)

Apply log rule:

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

lo g_{b} (x^{2} y) = lo g_{b} (x^{2}) + lo g_{b} (y)

= lo g_{b} (x^{2}) + lo g_{b} (y) - 4 lo g_{b} (z)

Apply log rule:

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

lo g_{b} (x^{2}) = 2 lo g_{b} (x)

= 2 lo g_{b} (x) + lo g_{b} (y) - 4 lo g_{b} (z)

lo g_{b} (\frac{9}{8})

ln (x^{2} - 7) - ln (x + 6) - 3

lo g_{5} (x - 2) + lo g_{5} (3 x + 7)

\frac{1}{2} ln (x + 3) - ln (x)

ln (9 e^{x})

What is expand log_{b}((x^2y)/(z^4)) ?
The solution to expand log_{b}((x^2y)/(z^4)) is 2log_{b}(x)+log_{b}(y)-4log_{b}(z)