What is ln(x^2y)-ln(y^2) ?

The solution to ln(x^2y)-ln(y^2) is ln((x^2)/y)

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simplify ln(x^2y)-ln(y^2)

simplify

ln (x^{2} y) - ln (y^{2})

ln (\frac{x ^{2}}{y})

Solution steps

ln (x^{2} y) - ln (y^{2})

Apply log rule:

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

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

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

Cancel the common factor:

y

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

- lo g_{10} (1.25 (1 0^{- 4}))

- lo g_{10} ((1.8 \cdot 1 0^{- 5}) (1))

ln (6 e^{m})

- \frac{1}{2} ln (\frac{1}{16}) + ln (\frac{1}{2})

ln (x^{4} y^{3})