What is ln(x^2)-ln(y^2)-ln(3) ?

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

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simplify ln(x^2)-ln(y^2)-ln(3)

simplify

ln (x^{2}) - ln (y^{2}) - ln (3)

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

Solution steps

ln (x^{2}) - ln (y^{2}) - ln (3)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

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

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