What is expand log_{e}(((x^2*y^3))/(z^4)) ?

The solution to expand log_{e}(((x^2*y^3))/(z^4)) is 2ln(x)+3ln(y)-4ln(z)

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expand log_{e}(((x^2*y^3))/(z^4))

expand

lo g_{e} (\frac{( x ^{2} \cdot y ^{3} )}{z ^{4}})

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

Solution steps

lo g_{e} (\frac{( x ^{2} y ^{3} )}{z ^{4}})

Apply log rule:

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

lo g_{e} (\frac{( x ^{2} y ^{3} )}{z ^{4}}) = lo g_{e} ((x^{2} y^{3})) - lo g_{e} (z^{4})

= lo g_{e} (x^{2} y^{3}) - lo g_{e} (z^{4})

Apply log rule:

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

lo g_{e} (z^{4}) = 4 lo g_{e} (z)

= lo g_{e} (x^{2} y^{3}) - 4 lo g_{e} (z)

Apply log rule:

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

lo g_{e} (x^{2} y^{3}) = lo g_{e} (x^{2}) + lo g_{e} (y^{3})

= lo g_{e} (x^{2}) + lo g_{e} (y^{3}) - 4 lo g_{e} (z)

Apply log rule:

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

lo g_{e} (x^{2}) = 2 lo g_{e} (x)

= 2 lo g_{e} (x) + lo g_{e} (y^{3}) - 4 lo g_{e} (z)

Apply log rule:

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

lo g_{e} (y^{3}) = 3 lo g_{e} (y)

= 2 lo g_{e} (x) + 3 lo g_{e} (y) - 4 lo g_{e} (z)

Simplify

lo g_{e} (x) : ln (x)

= 2 ln (x) + 3 lo g_{e} (y) - 4 lo g_{e} (z)

Simplify

lo g_{e} (y) : ln (y)

= 2 ln (x) + 3 ln (y) - 4 lo g_{e} (z)

Simplify

lo g_{e} (z) : ln (z)

= 2 ln (x) + 3 ln (y) - 4 ln (z)

ln (\frac{e ^{3}}{5})

ln (2) + ln (\frac{11}{4})

- lo g_{10} (1.7 \cdot 1 0^{5})

(0.63) ln (\frac{443}{680})

ln (11 y)

What is expand log_{e}(((x^2*y^3))/(z^4)) ?
The solution to expand log_{e}(((x^2*y^3))/(z^4)) is 2ln(x)+3ln(y)-4ln(z)