What is 2ln(x)+3ln(y)-5ln(z) ?

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (x^{9}) - \frac{1}{4} ln (x^{- 7})

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

lo g_{4} (\frac{2 x + 1}{3 y + 4})

\frac{1}{2} lo g_{b} (x) + 4 lo g_{b} (y) - 2 lo g_{b} (x)

1 - ln (\frac{2}{3})

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