What is ln((xy^2)/(z^4)) ?

The solution to ln((xy^2)/(z^4)) is ln(x)+2ln(y)-4ln(z)

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simplify ln((xy^2)/(z^4))

simplify

ln (\frac{x y ^{2}}{z ^{4}})

ln (x) + 2 ln (y) - 4 ln (z)

Solution steps

ln (\frac{x y ^{2}}{z ^{4}})

Apply log rule:

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

ln (\frac{x y ^{2}}{z ^{4}}) = ln (x y^{2}) - ln (z^{4})

= ln (x y^{2}) - ln (z^{4})

Apply log rule:

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

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

= ln (x y^{2}) - 4 ln (z)

Apply log rule:

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

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

= ln (x) + ln (y^{2}) - 4 ln (z)

Apply log rule:

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

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

= ln (x) + 2 ln (y) - 4 ln (z)

- lo g_{10} (1.4 \cdot 1 0^{- 9})

- ln (2) + 2 (ln (7) - ln (6))

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

ln (\frac{- x}{y - 2 x})

\frac{1}{3} (ln (a) + 3 ln (b)) - \frac{1}{2} (4 ln (c) - 2 ln (d))

What is ln((xy^2)/(z^4)) ?
The solution to ln((xy^2)/(z^4)) is ln(x)+2ln(y)-4ln(z)