What is expand log_{b}((x^2y)/(z^7)) ?

The solution to expand log_{b}((x^2y)/(z^7)) is 2log_{b}(x)+log_{b}(y)-7log_{b}(z)

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expand log_{b}((x^2y)/(z^7))

expand

lo g_{b} (\frac{x ^{2} y}{z ^{7}})

2 lo g_{b} (x) + lo g_{b} (y) - 7 lo g_{b} (z)

Solution steps

lo g_{b} (\frac{x ^{2} y}{z ^{7}})

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 ^{7}}) = lo g_{b} (x^{2} y) - lo g_{b} (z^{7})

= lo g_{b} (x^{2} y) - lo g_{b} (z^{7})

Apply log rule:

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

lo g_{b} (z^{7}) = 7 lo g_{b} (z)

= lo g_{b} (x^{2} y) - 7 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) - 7 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) - 7 lo g_{b} (z)

\frac{1}{5} ln (2)

3 lo g_{6} (x) + lo g_{6} (y)

lo g_{5} (x^{7})

lo g_{3} (13 z)

lo g_{10} (\frac{5 x}{y ^{2}})

What is expand log_{b}((x^2y)/(z^7)) ?
The solution to expand log_{b}((x^2y)/(z^7)) is 2log_{b}(x)+log_{b}(y)-7log_{b}(z)