What is 7ln(xy)-4ln(yz) ?

The solution to 7ln(xy)-4ln(yz) is ln((x^7y^3)/(z^4))

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simplify 7ln(xy)-4ln(yz)

simplify

7 ln (x y) - 4 ln (yz)

ln (\frac{x ^{7} y ^{3}}{z ^{4}})

Solution steps

7 ln (x y) - 4 ln (yz)

Apply log rule:

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

7 ln (x y) = ln ((x y)^{7})

= ln ((x y)^{7}) - 4 ln (yz)

Apply log rule:

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

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

= ln ((x y)^{7}) - ln ((yz)^{4})

Apply log rule:

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

ln ((x y)^{7}) - ln ((yz)^{4}) = ln (\frac{( x y ) ^{7}}{( yz ) ^{4}})

= ln (\frac{( x y ) ^{7}}{( yz ) ^{4}})

Simplify

\frac{( x y ) ^{7}}{( yz ) ^{4}} : \frac{x ^{7} y ^{3}}{z ^{4}}

= ln (\frac{x ^{7} y ^{3}}{z ^{4}})

ln (10) - ln (9)

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

lo g_{3} (\frac{x ^{4}}{3 y ^{3}})

ln (7) - ln (4)

ln (p^{4}) + ln (3 p^{5}) - 2 ln (p)