What is 7ln(xy)-5ln(yz) ?

The solution to 7ln(xy)-5ln(yz) is ln((x^7y^2)/(z^5))

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simplify 7ln(xy)-5ln(yz)

simplify

7 ln (x y) - 5 ln (yz)

ln (\frac{x ^{7} y ^{2}}{z ^{5}})

Solution steps

7 ln (x y) - 5 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}) - 5 ln (yz)

Apply log rule:

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

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

= ln ((x y)^{7}) - ln ((yz)^{5})

Apply log rule:

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

ln ((x y)^{7}) - ln ((yz)^{5}) = ln (\frac{( x y ) ^{7}}{( yz ) ^{5}})

= ln (\frac{( x y ) ^{7}}{( yz ) ^{5}})

Simplify

\frac{( x y ) ^{7}}{( yz ) ^{5}} : \frac{x ^{7} y ^{2}}{z ^{5}}

= ln (\frac{x ^{7} y ^{2}}{z ^{5}})

ln (- 0.5 t e^{- 0.5 t})

ln (3) + \frac{1}{2} ln (\frac{25}{9})

ln (e^{4} x^{8})

3 lo g_{10} (20.9) - lo g_{10} (30)

2.45 + lo g_{10} (\frac{0.055}{0.059})