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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{2} (\frac{p ^{3} q}{16 r ^{2}})

\frac{1}{3} ln (\frac{65}{76})

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

3 ln (3) - 4 ln (2) + 1

ln (x^{12} \frac{y ^{19}}{z ^{2}})

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