What is 2ln(x)+4ln(y)-3ln(z) ?

The solution to 2ln(x)+4ln(y)-3ln(z) is ln((x^2y^4)/(z^3))

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

simplify

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

ln (\frac{x ^{2} y ^{4}}{z ^{3}})

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

= ln (x^{2} y^{4}) - 3 ln (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln (x^{2} y^{4}) - ln (z^{3})

Apply log rule:

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

ln (x^{2} y^{4}) - ln (z^{3}) = ln (\frac{x ^{2} y ^{4}}{z ^{3}})

= ln (\frac{x ^{2} y ^{4}}{z ^{3}})

ln (x) + ln (3)

lo g_{3} (21) + lo g_{3} (10)

6 ln (x) - 4 ln (y)

(x - y ln (y) + y ln (x)) d x + x (ln (y) - ln (x)) d y

lo g_{5} (\frac{25}{y})

What is 2ln(x)+4ln(y)-3ln(z) ?
The solution to 2ln(x)+4ln(y)-3ln(z) is ln((x^2y^4)/(z^3))