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

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

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

simplify

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)

- 0.3 \cdot lo g_{2} (0.3) - 0.7 \cdot lo g_{2} (0.7)

14.77 + 10 lo g_{10} (\frac{179.68}{1.905})

ln (100) - ln (5) + ln (4)

2 lo g_{10} (a x) - lo g_{8} (2 x - 5)

ln (sin (x) x^{2} - 4)

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