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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

4 lo g_{9} (6) - lo g_{9} (3)

lo g_{9} (27) + lo g_{9} (3)

lo g_{18} (\frac{13 r}{s})

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

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