What is expand log_{b}((x^3y)/(z^4)) ?

The solution to expand log_{b}((x^3y)/(z^4)) is 3log_{b}(x)+log_{b}(y)-4log_{b}(z)

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Popular >

expand log_{b}((x^3y)/(z^4))

expand

lo g_{b} (\frac{x ^{3} y}{z ^{4}})

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

Solution steps

lo g_{b} (\frac{x ^{3} 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 ^{3} y}{z ^{4}}) = lo g_{b} (x^{3} y) - lo g_{b} (z^{4})

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

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

= 3 lo g_{b} (x) + lo g_{b} (y) - 4 lo g_{b} (z)

lo g_{9} (5 x)

lo g_{9} (4 n p^{3})

lo g_{9} (6) + \frac{1}{2} \cdot lo g_{9} (a) + \frac{1}{2} \cdot lo g_{9} (b)

\frac{1}{2} [4 ln (x + 1) + ln (x) - ln (x^{4} - 3)]

ln (\frac{6}{x ^{2} + 1})

What is expand log_{b}((x^3y)/(z^4)) ?
The solution to expand log_{b}((x^3y)/(z^4)) is 3log_{b}(x)+log_{b}(y)-4log_{b}(z)