What is ln((x^3y^2)/(z^5)) ?

The solution to ln((x^3y^2)/(z^5)) is 3ln(x)+2ln(y)-5ln(z)

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simplify ln((x^3y^2)/(z^5))

simplify

ln (\frac{x ^{3} y ^{2}}{z ^{5}})

3 ln (x) + 2 ln (y) - 5 ln (z)

Solution steps

ln (\frac{x ^{3} y ^{2}}{z ^{5}})

Apply log rule:

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

ln (\frac{x ^{3} y ^{2}}{z ^{5}}) = ln (x^{3} y^{2}) - ln (z^{5})

= ln (x^{3} y^{2}) - ln (z^{5})

Apply log rule:

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

ln (z^{5}) = 5 ln (z)

= ln (x^{3} y^{2}) - 5 ln (z)

Apply log rule:

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

ln (x^{3} y^{2}) = ln (x^{3}) + ln (y^{2})

= ln (x^{3}) + ln (y^{2}) - 5 ln (z)

Apply log rule:

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

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

= 3 ln (x) + ln (y^{2}) - 5 ln (z)

Apply log rule:

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

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

= 3 ln (x) + 2 ln (y) - 5 ln (z)

- ln (\frac{2.8}{5}) \cdot 52.41

ln (- \frac{5}{4} e^{4 x})

3 (ln (3 e))^{2} + 2 ln (3 e)

- lo g_{10} (1.5 \cdot 1 0^{- 9})

ln (4 (x^{2} - 4 x + 6)^{3})

What is ln((x^3y^2)/(z^5)) ?
The solution to ln((x^3y^2)/(z^5)) is 3ln(x)+2ln(y)-5ln(z)