What is expand log_{b}((x^3y)/(z^2)) ?

The solution to expand log_{b}((x^3y)/(z^2)) is 3log_{b}(x)+log_{b}(y)-2log_{b}(z)

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expand log_{b}((x^3y)/(z^2))

expand

lo g_{b} (\frac{x ^{3} y}{z ^{2}})

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

Solution steps

lo g_{b} (\frac{x ^{3} y}{z ^{2}})

Apply log rule:

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

lo g_{b} (\frac{x ^{3} y}{z ^{2}}) = lo g_{b} (x^{3} y) - lo g_{b} (z^{2})

= lo g_{b} (x^{3} y) - lo g_{b} (z^{2})

Apply log rule:

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

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

= lo g_{b} (x^{3} y) - 2 lo g_{b} (z)

Apply log rule:

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

lo g_{b} (x^{3} y) = lo g_{b} (x^{3}) + lo g_{b} (y)

= lo g_{b} (x^{3}) + lo g_{b} (y) - 2 lo g_{b} (z)

Apply log rule:

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

lo g_{b} (x^{3}) = 3 lo g_{b} (x)

= 3 lo g_{b} (x) + lo g_{b} (y) - 2 lo g_{b} (z)

ln (\frac{x ^{2} - 1}{x ^{7}})

lo g_{3} (2 x) - lo g_{3} (x - 2)

6 ln (2) - 4 ln (y)

5 ln (x - 2) - ln (x + 2) - 3 ln (x)

ln (7 e^{x})

What is expand log_{b}((x^3y)/(z^2)) ?
The solution to expand log_{b}((x^3y)/(z^2)) is 3log_{b}(x)+log_{b}(y)-2log_{b}(z)