What is 2ln(x)+4ln(y)-5ln(z) ?

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{4} (5 x y)

lo g_{b} (x^{2} y^{3})

- \frac{1}{2} ln ∣ x + 1 ∣ + \frac{1}{2} ln ∣ x - 1 ∣

lo g_{6} (\frac{1}{z ^{3}})

lo g_{6} (\frac{64 x ^{3} ( 4 x + 1 )}{2 x - 1})

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