What is expand ln((2y^2)/(z^3)) ?

The solution to expand ln((2y^2)/(z^3)) is ln(2)+2ln(y)-3ln(z)

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expand ln((2y^2)/(z^3))

expand

ln (\frac{2 y ^{2}}{z ^{3}})

ln (2) + 2 ln (y) - 3 ln (z)

Solution steps

ln (\frac{2 y ^{2}}{z ^{3}})

Apply log rule:

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

ln (\frac{2 y ^{2}}{z ^{3}}) = ln (2 y^{2}) - ln (z^{3})

= ln (2 y^{2}) - ln (z^{3})

Apply log rule:

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

ln (z^{3}) = 3 ln (z)

= ln (2 y^{2}) - 3 ln (z)

Apply log rule:

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

ln (2 y^{2}) = ln (2) + ln (y^{2})

= ln (2) + ln (y^{2}) - 3 ln (z)

Apply log rule:

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

ln (y^{2}) = 2 ln (y)

= ln (2) + 2 ln (y) - 3 ln (z)

2 lo g_{3} (0.5) + 2 lo g_{3} (5) - 2 lo g_{3} (\frac{5}{6})

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

0.94 \cdot ln (3 \cdot 1 0^{6}) + 0.06 ln (6000)

ln (\frac{39}{51})

ln (\frac{6}{π ^{2}})

What is expand ln((2y^2)/(z^3)) ?
The solution to expand ln((2y^2)/(z^3)) is ln(2)+2ln(y)-3ln(z)