What is ln((x^4y^2)/(z^5)) ?

The solution to ln((x^4y^2)/(z^5)) is 4ln(x)+2ln(y)-5ln(z)

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simplify ln((x^4y^2)/(z^5))

simplify

ln (\frac{x ^{4} y ^{2}}{z ^{5}})

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

Solution steps

ln (\frac{x ^{4} y ^{2}}{z ^{5}})

Apply log rule:

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

ln (\frac{x ^{4} y ^{2}}{z ^{5}}) = ln (x^{4} y^{2}) - ln (z^{5})

= ln (x^{4} 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^{4} y^{2}) - 5 ln (z)

Apply log rule:

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

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

= ln (x^{4}) + ln (y^{2}) - 5 ln (z)

Apply log rule:

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

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

= 4 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)

= 4 ln (x) + 2 ln (y) - 5 ln (z)

ln (\frac{z}{x ^{8} y})

ln (3) + ln (4) - ln (6)

- lo g_{10} (3.49 \cdot 1 0^{- 3})

ln (2 \cdot x) - x^{2} + 5

ln (\frac{66}{51}) \cdot 5

What is ln((x^4y^2)/(z^5)) ?
The solution to ln((x^4y^2)/(z^5)) is 4ln(x)+2ln(y)-5ln(z)