What is expand ln((x^4sqrt(y))/(z^6)) ?

The solution to expand ln((x^4sqrt(y))/(z^6)) is 4ln(x)+ln(sqrt(y))-6ln(z)

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expand ln((x^4sqrt(y))/(z^6))

expand

ln (\frac{x ^{4} y}{z ^{6}})

4 ln (x) + ln (y) - 6 ln (z)

Solution steps

ln (\frac{x ^{4} y}{z ^{6}})

Apply log rule:

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

ln (\frac{x ^{4} y}{z ^{6}}) = ln (x^{4} y) - ln (z^{6})

= ln (x^{4} y) - ln (z^{6})

Apply log rule:

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

ln (z^{6}) = 6 ln (z)

= ln (x^{4} y) - 6 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) - 6 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) - 6 ln (z)

2 ln (6) - 3 ln (8)

lo g_{10} (\frac{5 x y ^{2}}{z ^{3}})

ln (\frac{6.1 \cdot 7.36}{9.42 \cdot 1 0 ^{- 3}})

4 lo g_{10} (x) + 2 lo g_{10} (x - 1)

\frac{5 ln ( - 1 )}{6} - 3 \frac{1}{3}

What is expand ln((x^4sqrt(y))/(z^6)) ?
The solution to expand ln((x^4sqrt(y))/(z^6)) is 4ln(x)+ln(sqrt(y))-6ln(z)