What is expand ln((x^4sqrt(y))/(z^5)) ?

The solution to expand ln((x^4sqrt(y))/(z^5)) is 4ln(x)+ln(sqrt(y))-5ln(z)

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expand ln((x^4sqrt(y))/(z^5))

expand

ln (\frac{x ^{4} y}{z ^{5}})

4 ln (x) + ln (y) - 5 ln (z)

Solution steps

ln (\frac{x ^{4} y}{z ^{5}})

Apply log rule:

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

ln (\frac{x ^{4} y}{z ^{5}}) = ln (x^{4} y) - ln (z^{5})

= ln (x^{4} y) - ln (z^{5})

Apply log rule:

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

ln (z^{5}) = 5 ln (z)

= ln (x^{4} y) - 5 ln (z)

Apply log rule:

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

ln (x^{4} y) = ln (x^{4}) + ln (y)

= ln (x^{4}) + ln (y) - 5 ln (z)

Apply log rule:

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

ln (x^{4}) = 4 ln (x)

= 4 ln (x) + ln (y) - 5 ln (z)

lo g_{5} (\frac{125}{x + 3})

lo g_{b} (y^{6} x)

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

lo g_{9} (\frac{z}{81})

lo g_{5} ((u v^{5})^{2})

What is expand ln((x^4sqrt(y))/(z^5)) ?
The solution to expand ln((x^4sqrt(y))/(z^5)) is 4ln(x)+ln(sqrt(y))-5ln(z)