What is ln((xy^4)/(z^3)) ?

The solution to ln((xy^4)/(z^3)) is ln(x)+4ln(y)-3ln(z)

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simplify ln((xy^4)/(z^3))

simplify

ln (\frac{x y ^{4}}{z ^{3}})

ln (x) + 4 ln (y) - 3 ln (z)

Solution steps

ln (\frac{x y ^{4}}{z ^{3}})

Apply log rule:

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

ln (\frac{x y ^{4}}{z ^{3}}) = ln (x y^{4}) - ln (z^{3})

= ln (x y^{4}) - ln (z^{3})

Apply log rule:

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

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

= ln (x y^{4}) - 3 ln (z)

Apply log rule:

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

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

= ln (x) + ln (y^{4}) - 3 ln (z)

Apply log rule:

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

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

= ln (x) + 4 ln (y) - 3 ln (z)

ln (\frac{2}{2 \cdot ( 1.42 \cdot 1 0 ^{(- 3)} )})

ln (\frac{1}{m} e^{\frac{- ( x - 2 )}{m}})

- 6 ln (2) + \frac{15}{2} - 6 (ln (3) - ln (2)) + \frac{7}{2}

lo g_{4} (x^{2} - 11 x + 28) - lo g_{4} (x - 7)

- 3 lo g_{7} (x) + 5 lo g_{7} (y) - lo g_{3} (z)

What is ln((xy^4)/(z^3)) ?
The solution to ln((xy^4)/(z^3)) is ln(x)+4ln(y)-3ln(z)